The employment of caloric-effect materials for solid-state heat pumping

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The Employment of Caloric-Effect Materials for Solid-State Heat Pumping C. Aprea Member of IIR-IIF Commission E2 , A. Greco , A. Maiorino Member of IIR-IIF , C. Masselli Member of IIR-IIF Commission B2 PII: DOI: Reference:

S0140-7007(19)30396-2 https://doi.org/10.1016/j.ijrefrig.2019.09.011 JIJR 4527

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

20 March 2019 5 September 2019 16 September 2019

Please cite this article as: C. Aprea Member of IIR-IIF Commission E2 , A. Greco , A. Maiorino Member of IIR-IIF , C. Masselli Member of IIR-IIF Commission B2 , The Employment of Caloric-Effect Materials for Solid-State Heat Pumping, International Journal of Refrigeration (2019), doi: https://doi.org/10.1016/j.ijrefrig.2019.09.011

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Highlights   

A map of the energy performances of a caloric heat pump was drawn. The heat pump was evaluated while working with different caloric effect materials. Globally, mechanocaloric is the most suitable effect to be employed for heat pump.

1

THE EMPLOYMENT OF CALORIC-EFFECT MATERIALS FOR SOLID-STATE HEAT PUMPING C. Aprea1,a, A. Greco2, A. Maiorino1,c, C. Masselli1,b,* 1

Department of Industrial Engineering, University of Salerno, Via Giovanni Paolo II 132, 84084, Fisciano (SA), Italy

2

Department of Industrial Engineering, University of Naples Federico II, P.le Tecchio 80, 80125, Napoli, Italy a

Member of IIR-IIF Commission E2

b

Member of IIR-IIF Commission B2 c

Member of IIR-IIF

* Corresponding author: e-mail [email protected] Abstract In this paper we draw a map of the energy performances of a solid-state caloric heat pump working with different caloric-effect materials. The investigation is performed considering a number of various caloric effect materials and employing them in a caloric heat pump based on Active Caloric Regenerative heat pumping cycle. The tests were performed through a 2Dimensional model, already validated in previous investigations, solved with Finite Element Method. The employed materials selected are electrocaloric and mechanocaloric; gadolinium, the benchmark magnetocaloric material, was also tested for comparative purposes. We evaluated the energy performances of the heat pump as temperature span, heating power and coefficient of performance. From global considerations based on the simultaneous evaluation of these three energy parameters, we consider mechanocaloric as the most suitable caloric effect to be employed for heat pump applications, especially with reference to the elastocaloric Ni-Ti and to the barocaloric Acetoxy Silicone Rubber, since their heating powers with respect to the energy expenses required, give satisfying coefficients of performance and temperature spans. Keywords: Caloric heat pump; caloric materials; elastocaloric effect; electrocaloric effect; barocaloric effect; energy performances.

2

Nomenclature Roman symbols B

magnetic field induction, T

C

specific heat, J kg-1 K-1

COP

coefficient of performance, -

E

electric field, V.m-1

G

mass flux, kg s-1 m-2

k

thermal conductivity, W m-1 K-1

L

length of the regenerator in fluid flow direction, mm ̇

flow rate, kg s-1

n

number of times

p

pressure, Pa

Q

power density associated to caloric effect, W m-3

̇

power, W

T

temperature, K

t

time, s

u

longitudinal fluid velocity, m s-1

v

orthogonal fluid velocity, m s-1 ̇

mechanical power, W

x

longitudinal spatial coordinate, m

Y

applied driving field

y

orthogonal spatial coordinate, m

Greek symbols Δ

finite difference

δ

infinitesimal difference ̅

η

infinitesimal quantity efficiency 3

𝜃

period of ACR cycle, s

ν

kinematic viscosity, m2 s-1

ρ

density, kg m-3

σ

stress, Pa



period of each step of ACR cycle, s

Subscripts 0

minimum

1

maximum

ad

adiabatic

C

cold

FD

field decreasing

f

fluid

H

hot

ICM

Inverse Carnot Machine

max

at maximum

ref

refrigeration

s

solid

span

span across ACR cold and hot side

TOT

total

Acronyms ACR

Active Caloric Regenerative heat pump

ASR

Acetoxy Silicone Rubber

BCE

BaroCaloric Effect

CHEX

Cold Heat EXchanger

ECE

ElectroCaloric Effect

eCE

elastoCaloric Effect 4

HFC

hydrofluorocarbons

HHEX

Hot Heat Exchanger

HTF

Heat Transfer Fluid

HVAC

Heating Ventilation & Air Conditioning

MCE

MagnetoCaloric Effect

NIK

Not-In-Kind

PBZ

Pb0.8Ba0.2ZrO3

PLZST

Pb0.97La0.02(Zr0.75Sn0.18Ti0.07)O3

VNR

Vulcanized Natural Rubber

VSR

Vulcanizing Silicone Rubbers

1. Introduction Is it possible to change the way of refrigerating, air conditioning and heat pumping? Are there new frontiers to be overcome? These questions are the core of many government and scientific round tables. Changing the way to cool and air condition has been a hot topic for three decades since in 1987 (Montreal Protocol, 1987), with the issue of Montreal Protocol, the first countermeasures were taken to fight ozone depletion and, subsequently, global warming. The commitment to counteract the warming world problem has been renewed over the years with Kyoto Protocol (Kyoto Protocol, 1997), up to the Kigali amendment in 2016 (Heath, 2017), with the focus of trying to make vapor compression more environmentally friendly, by reducing the usage of hydrofluorocarbons (HFC). Next to this, many research groups of universities, laboratories and companies, are trying to answer to the second question: they want to overtake new frontiers of the concept of refrigerating, air conditioning and heat pumping. Therefore, over the last decades a huge number of Not-InKind (NIK) technologies: in 2012 Bansal et al. reviewed the state of the art, in 2012, of Not-In-Kind refrigeration for household applications (Bansal et al., 2012); in 2014 Brown et al. proposed a comprehensive review of alternative cooling technologies (Brown and Domanski, 2014) whereas Goetzler et al. presented a report underlining the potentialities of Non Vapor-Compression HVAC technologies in energy saving (Goetzler et al., 2014); in 2016 Qian et al. summarized Not-In-Kind cooling technologies comparing refrigerants and system performances (Qian et al., 2016). In the Not-In-Kind scenario, a significative growth of studies and investigations based on caloric cooling and heat pumping has been registered; in 2012 two interesting review on materials were published: Smith et al. reviewed (Smith et al., 2012) the magnetocaloric materials for improving the performance of the prototypes, whereas Fähler et al. summarized (Fähler et al., 2012) the main concepts on caloric effect materials for cooling. The most comprehensive and general review on caloric cooling and heat pumping was published in 2015 by 5

Kitanovski et al. (Kitanovski et al., 2015a) where the main concepts related to all the caloric technologies were underlined. In 2016, Aprea et al. (Aprea et al., 2016a) gave a focus about the energy performances of the electrocaloric materials in an active electrocaloric cooler. In 2017, an exhaustive investigation about an integrated solid state elastocaloric heat pumping system was published by Luo et al. (Luo et al, 2017). In 2018 Johra et al. investigated the realization on an active magnetocaloric heat pump (Johra et al., 2018a) and its integration in a residential building (Johra et al., 2018b). Caloric cooling belongs to solid-state refrigeration and Heating Ventilation & Air Conditioning (HVAC) technologies and it is based on different thermo-physical effects (counting mechanocaloric, electrocaloric and magnetocaloric effects) of solid-state caloric materials employed as refrigerants. Such materials exploit the property to change their temperature (∆Tad) as a consequence of an adiabatic variation of the intensity of the external applied driving field (Aprea et al., 2018a). This technology has the advantage to not employ greenhouse gases that are damaging for the environment and to global warming. It can operate with small level of noise and it exhibits the potential of recycling its components (Smith et al., 2012). All these advantages confer to caloric refrigeration the role to potentially become a real alternative to the conventional vapor compression refrigeration. Based on the state-of the art of the works published in literature until now, many investigations focused on caloric refrigeration with studies both numerical and experimental finalized to the development of caloric refrigerators. Among the numerical studies, Aprea et al. offered (Aprea et al., 2013) a wide study on first and second order magnetocaloric effect materials employed as refrigerants in an active magnetocaloric cooler. In 2015, Qian et al. introduced (Qian et al, 2015) a numerical model for thermoelastic cooling systems whereas Chauhan analyzed the elastocaloric effect for solid-state refrigeration device (Chauhan et al., 2015). A further novel model of an elastocaloric cooler was introduced in 2017 by Qian et al. (Qian et al., 2017). In 2018, Krašna et al. introduced (Krašna et al., 2018) a numerical model on first order phase transition electrocaloric materials; whereas a variable load control strategy for magnetocaloric devices was presented by Qian et al. (Qian et al., 2018). Several models were validated experimentally with caloric prototypes in order to become a tool for the optimization of the experimental systems (Kitanovski et al., 2015b; Aprea et al., 2017, 2018b; Plaznik et al., 2019). Consequently, until now, a substantial number of prototypes of caloric coolers has been developed in the world (Aprea et al., 2016b, 2016c; Blumenthal and Raatz, 2016; Engelbrecht et al., 2017; Greco et al., 2019). Less space was given, up to now, to the application of this technology for heat pumping purposes. By the way, recent investigations confirmed the potential of exploiting caloric effects for realizing heat pumping systems. In 2015, Moya et al. published (Moya et al., 2015) a related point-of-view paper and Ossmer et al. (Ossmer et al., 2015) presented an elastocaloric heat pump based on a shape memory alloy foil system. In 2017 a magnetocaloric heat pump based on Peltier thermal diodes was introduced by de Vries et al. (de Vries et al., 2017). In 2018, a study devoted to the development of an electrocaloric heat pump was introduced by Chen et al. (Chen et al., 2018), whereas Zimm et al. presented (Zimm et al., 2018) a paper on the evolution of magnetocaloric heat pump systems. Literature accounts of magnetocaloric (Hull and Uherka, 1989; Vuarnoz et al., 2007; Benedict et al., 2016), electrocaloric (Smullin et al., 2015) and elastocaloric heat pumps 6

(Tušek et al., 2016) in which the results of the investigations are published with respect to the test on a single or a couple of materials showing the same type of caloric effect. Gadolinium (Gd) (Benedict et al., 2016; Johra et al., 2018a) and NiTi (Tušek et al., 2016; Luo et al., 2017) alloys are currently the most investigated as materials employed in magnetocaloric or elastocaloric heat pumping applications, respectively. Therefore, there are no contributions showing and comparing globally the effect of testing more caloric materials with different caloric effects and, furthermore, there are currently no publications on barocaloric heat pumps. The aim of the investigation introduced in this paper is to fill this gap, providing an overview of the result collected by employing a wide set of different-effects caloric materials, including barocaloric ones, in an active caloric heat pump. The main purpose of this work is to provide, on equal operating conditions, comparison metrics that can allow the identification of the strengths and weaknesses of each caloric effect material.

2. Caloric heat pump description The caloric heat pump object of investigation is based on the Active Caloric Regenerative heat pump (ACR) cycle that is a Brayton-based cycle in which the caloric material acts both as refrigerant and as regenerator of the heat pump system. A detailed description of the ACR cycle for heat pump applications is reported in the following paragraph. The four processes of the cycle are reported in Figure 1.

Figure 1. The Active Caloric Regenerative heat pump cycle: a) adiabatic field-falling; b) HHEX to CHEX transferring; c) adiabatic field-growing; d) CHEX to HHEX transferring. 7

In Figure 1 one can observe the four ACR processes that lead to the desired effect of the cycle: pumping heat to in house by taking it from the external environment which is colder. Starting from a condition in which, in the ACR regenerator, the external field Y is applied and kept at maximum (Y1), the first step (Figure 1(a)) sees an adiabatic reduction of it until reaching the minimum (Y0). Therefore, the caloric material exhibits the caloric effect and a decrease of its temperature is registered. Then, the auxiliary fluid flows from the hotter (HHEX) to the colder heat exchanger (CHEX), crossing the regenerator and consequently heating it (Figure 1(b)). By increasing, adiabatically, the external field from Y0 to Y1 (Figure 1(c)), a further heating of the regenerator is registered due to caloric effect. Hence, the fluid is heated (Figure 1(d)) because of crossing the regenerator from CHEX to HHEX where it adds heat, producing the desired effect of ACR cycle. 3. Performance analysis and parameters selection The aim of this section is to illustrate in detail the structure of the analysis performed and reported in this paper. The following deals with the main aspects as the selection of the materials for heat pump application, the followed methodology, the description of the parameters through which we evaluate the energy performances of the heat pump system. 3.1 Materials selection A wide set of caloric materials was selected for the investigation and numerous are the variables and the parameters that influenced the choice. Substantially, the discriminating factors adopted had to ensure that the materials are: 

exhibiting high caloric effect and low specific heat (to promote the heat exchange rather than heat accumulation) in temperature range suitable for heat pump application.



easily manufactured, low-cost and non-toxic, in order to allow a future industrial production for commercialization.

Moreover, the intention was to build a performance map that embraced as many cases as possible. For this reason, electrocaloric, elastocaloric and barocaloric materials were chosen. In addition, also the magnetocaloric benchmark, gadolinium (Gd), for comparative purposes, was selected and calculated. In the number of barocaloric materials object of investigation, also the barocaloric elastomers were considered. For uniformity of presentation with respect to the results collected, we decided to divide the materials into three subgroups: (a) electrocaloric and magnetocaloric; (b) mechanocaloric materials (group 1) and (c) mechanocaloric materials (group 2). Especially, the last group embraces the barocaloric elastomers. Next to gadolinium, the magnetocaloric rare-earth that shows 6 K as peak of ∆Tad due to magnetocaloric effect at 294 K under ∆B = 1.5 T (Dan’Kov et al., 1998), in the first group we considered the following two giant electrocaloric effect materials: 

a thin film of relaxor ferroelectric Pb0.8Ba0.2ZrO3 (PBZ) (Peng et al., 2013), deposited on a Pt(111)/TiOx/SiO2/Si substrate, in which the antiferroelectric and ferroelectric phases coexists at 8

room temperature, in correspondence of which it presents a peak (290 K). The selected field intensities are ∆E = 59.8 MV m-1 and ∆E = 40.8 MV m-1 that provide respectively a maximum ∆Tad of 45 K and 36 K. 

Pb0.97La0.02(Zr0.75Sn0.18Ti0.07)O3 (PLZST) (Zhao et al., 2015), deposited on LaNiO3/Si (100) substrate that exhibits an antiferroelectric nature with a maximum giant ECE at 278 K, in correspondence to a field-induced antiferroelectric to ferroelectric phase transition. Moreover, ∆Tad remains very high in the range [278; 298] K, making PLZST definitely suitable for heat pump applications. Specifically, they were considered under electric changes of 90 MVm-1 and 70 MV m-1.

Among the selected mechanocaloric materials, group 1 embraces: 

the elastocaloric Ni-Ti polycrystals (Tušek et al., 2015), benchmark of elastocaloric systems, showing a peak at 350 K but anyway exhibiting a remarkable elastocaloric effect in temperature range devoted to heat pump application. The considered stress field change is 0.9 GPa which results in a peak of 25 K as adiabatic temperature change due to elastocaloric effect.



The barocaloric oxyfluorides (NH4)2MoO2F4 (Gorev et al., 2010) showing a maximum direct barocaloric effect at 272 K which remains remarkable until 360 K. This ensure a good applicability for heat pump purposes. Two are the considered intensities of the pressure field: 0.9 GPa and 0.7 GPa. Such variations ensure maximum due to barocaloric effect of 18 K and 15 K, respectively.



The inverse barocaloric MnCoGe0.99In0.01 (Wu et al., 2015) exhibiting a pressure-driven orthorhombic-hexagonal magneto-structural transition at 298 K which, for ∆p = 0.3 GPa, ensures a maximum ∆Tad of around 18 K.

The group 2 of mechanocaloric materials focuses on barocaloric elastomers since we want this investigation to provide a focus also on the elastomeric vulcanizing rubbers. They are soft materials that can be accounted potentially as performing mechanocaloric materials because of the coupling of their elastomeric properties with promising structural transitions. Among them, interest has aroused a group named Vulcanizing Silicone Rubbers (VSR) at room temperature, made of polydimethylsiloxane, additive, preserving agent and fillers. Next to them, also the natural rubber seems to be promising because of the high caloric performances, low cost and environmental impact. Indeed, the group 2 of mechanocaloric materials accounts the following ones: 

Acetoxy Silicone Rubber (ASR), a VSR that exhibits a supergiant (Imamura et al., 2017) barocaloric effect with a peak of ∆Tad located in correspondence of the crystalline– amorphous transitions and also polymer chains rearrangements. VSR was investigated under ∆p = [0.173; 0.273; 0.390] GPa providing associated maximum ∆Tad of about [22; 30; 41] K that shift to higher temperatures when the pressure increases.



The Vulcanized Natural Rubber (VNR) (Usuda et al., 2017) processed from a liquid pre-vulcanized latex that shows ∆Tad of about 11 K under an adiabatic pressure change of ∆p = 0.173 GPa. 9

For further details, Table 1 contains the main thermal and caloric parameters proper of the caloric materials object of investigation. Material

Tpeak

Δfield

ΔTad,max

ρ

k

Caloric

[kg/m ]

[W/mK]

effect

7900

10.9

MCE

3

[K]

Ref.

[K] Gadolinium

294

1.5 T

6

(Dan’Kov et al., 1998)

Pb0.8Ba0.2ZrO3

290

Pb0.97La0.02(Zr0.75Sn0.1 8Ti0.07)O3

278

NiTi

350

59.8 MV/m

45

40.8 MV/m

36

90

54

70

43

0.9 GPa

26

7700

1

ECE

(Peng et al., 2013)

8300

1

ECE

(Zhao et al., 2015)

6500

10

eCE

(Tušek

et

al., 2015) (NH4)2MoO2F4

MnCoGe0.99In0.01

272

0.9 GPa

18

272

0.7 GPa

15

298

0.3 GPa

18.3

2200

1

BCE

(Gorev

et

al., 2010) 7900

65

BCE

(Wu et al., 2015)

ASR

298

0.390 GPa

41.1

960

1.48

BCE

(Wang et

273

0.273 GPa

30

al., 2003;

252

0.173 GPa

22

Imamura et al., 2017)

V-NR

333

0.173 GPa

11.1

930

0.13

BCE

(Usuda et al., 2017)

Table 1. Main features of the caloric materials under investigation.

3.2 Methodology All the materials selected in section 3.1 were investigated as working material of a caloric heat pump on equal operative conditions (described in detail in section 3.3). The behaviour of the caloric heat pump is regulated by a two-dimensional numerical model, already introduced in another our investigation (Aprea et al., 2018a) and experimentally validated with an already existing caloric prototype (Aprea et al., 2015, 2018b). The ACR heat pump is composed by a parallel-plate regenerator (H x L = 20 x 45 mm2) made of 54 slices of caloric material (0.25 mm thickness of each slice) separated by channels (0.125 mm thickness of each one) in which the Heat Transfer Fluid (HTF), water, crossing the regenerator along a length L, has the final purpose to add heat to the indoor room, connected by a hot heat exchanger at TH. The cold heat exchanger is coupled with the outdoor environment, whose temperature is TC. We designed the present geometry with the common goal of making it suitable for each caloric effect materials. Specifically, we decided to work with a parallel-plate geometry also to make it suitable for both 10

electrocaloric and mechanocaloric applications. As an example, working with a parallel-plate geometry allows the connection of the electrodes necessary to generate the electric field (in a real system); on the other side, a cylindric geometry that would result suitable for mechanocaloric, would not allow easily the application of the electric field for electrocaloric materials. Furthermore, the dimensions of the envelope of the regenerator were chosen accordingly to the ones of the experimental prototype that the model was validated with (Aprea et al., 2015, 2018b). The number of parallel plates was chosen to work with the same volume ratio of the regenerator of the experimental prototype that we developed in our laboratory (Aprea et al., 2015). Below is reported the structure of the mathematical model that describes the four processes of the ACR cycle:

(

)

(

)

(

)

(

{

)

(

{

)

( (

(2)

) )

(1)

(

)

(

)

(3)

The system of (1) rules the HTF-crossing phases whereas (2) describes the adiabatic applying-removing processes of the external forcing-field. During the HTF-crossing phases, the interaction among the regenerator and the cold and hot heat exchangers is regulated by Dirichlet boundary conditions: in the coldto-hot HTF-crossing phase the CHEX mean temperature TC is imposed in the left side; in the hot-to-cold TH is forced on the right side. During the adiabatic field-changing phases the coupled boundary condition is thermal insulation to all the boundaries. The term Q, explained in (3), converts the caloric effect into a power density. Since Q is a function of the field and the temperature, its mathematical expression was obtained by the help of a mathematical finder software (i.e. a software able to convert a table to a mathematical function, finding the most appropriate mathematical expression), as a result of elaboration and manipulation of experimental data of Cs(field, Ts) and ∆Tad(field, Ts), coming from scientific literature. Cs is generally defined as Cs(field, Ts) but we considered such dependence only for gadolinium where the data about the correlation of the specific heat with the magnetic field intensity were provided in open literature. For the other materials we considered the specific heat constant with the field variation, according to the values provided by scientific community. Further 11

details about building Q terms are reported in Aprea et al. (Aprea et al., 2018b) where the construction, the application during field increasing/decreasing processes and the way to account the hysteresis phenomenon, are exhaustively explained. As an example, Figures 2(a) (b) (c) exhibit the ASR Q-functions during decompression for ∆p = [0.173; 0.273; 0.390] GPa. One can see the increasing magnitude of the peak together with the pressure field, as a consequence of the increasing of the barocaloric effect in terms of ∆Tad. The dots represent the points coming from scientific literature, whereas the red curve is the mathematical fitting of them by the function findersoftware that gives also the corresponding mathematical expression for each Q. The model is solved with Finite Element Method and the ACR cycle runs cyclically several times until reaching steady-state that is satisfying the cyclicality criterion in every point of the ACR regenerator: { (

𝜃)

(

𝜃)}

̅

(4)

12

Figure 2. for the barocaloric elastomer Acetoxy-Silicone Rubber Q-functions built for adiabatic decompression process in the range: (a) [0.173; 0] GPa; (b) [0.273; 0] GPa; (c) [0.390; 0] GPa.

3.3 Aim of the analysis The present investigation aims to draw a map of the energy performances of a caloric heat pump working with multiple materials showing different caloric effects. The investigation was performed considering [298; 278] K as indoor-outdoor temperature range and 0.8 s as time period 𝜃 of ACR cycle, since every process lasts 0.2 s. Mass flux of the heat transfer fluid was varied in the range [150; 250] kg s-1m-2. The adiabatic variations of the external fields applied, necessary so that the caloric effect manifests itself as a temperature change, were chosen with reference to the singular caloric material under test, in order to get ∆Tad compatible with the working range of a heat pump. The map of the energy performances was drawn basing on the following energy parameters: ∫

(

)

(5)

∆Tspan is the temperature span measured across the regenerator at the end of the “CHEX to HHEX transferring” process. 13

̇

( ( ̇

∫

)

)

(6)

̇ is the heating power of the caloric heat pump: it measures the power at which the system pumps heat. ̇

=

̇

̇ ̇

̇ ̇

̇

̇

(7) OP is the coefficient of performance of the heat pump and it is conceived as the ratio between the heating power of the pump and the total expense made to get it.

̇

embraces two contributions:

accounts the power needed to vary the external field for caloric effect manifesting; ̇

̇

that

is the contribution

associated to the mechanical power required to make the heat-transfer fluid crossing the regenerator in both directions. ̇ ̇ ̇ where ̇ ̇

̇

(8)

is the power associated to the heat taken from the cold environment: ̇

∫ ̇

was evaluated through:

(

(

))

(9)

̇

was calculated according to the following equation. ̇ (∆

∆

)

(10)

4. Results collected and discussion The results presented in this section were collected with the ACR heat pump working in steady-state conditions under the operative conditions enounced in section 3.3. Therefore, the heat pump experiments cyclically the four steps of the ACR cycle. Every step takes as initial condition the final temperature distribution of the previous step. In Figure 3 one can appreciate the temperature profiles of a slice of the parallel-plate regenerator, working with Ni-Ti, during the four processes of the ACR cycle. The inherent operative conditions are: ∆σ = [0;0.390] GPa as field variation; 150 kg m-2 s-1 as fluid mass flux. In particular, in the figure each profile is referred at the end of each process that constitutes, also, the initial condition of the following phase. The left side of the regenerator is connected to the cold heat exchanger whereas the right side with the hot one and, therefore, with the indoor environment to be heated. Moreover, taking as starting point the plotted profile of step IV (it is also the starting point for step I) and as final point the step I, one can see that the effect of adiabatically field removing does not determine a uniform temperature decrease, since the magnitude of caloric effect is a function of the starting temperature.

14

Figure 3. Temperature profiles of a slice of the ACR regenerator of the caloric heat pump, working with NiTi under ∆σ = [0; 0.9] GPa and Gf = 150 kg m-2 s-1.

Figure 4. Velocity field in a channel of the parallel-plate regenerator during the (a) hot-to-cold; (b) cold-tohot fluid flow processes. Figure 4 reports the zooms of the velocity fields established in a channel during the (a) hot-to-cold and (b) cold-to-hot fluid flowing processes of the ACR cycle with NiTi, in the same conditions of Figure 3 (∆σ = [0; 0.390] GPa as field variation; Gf = 150 kg m-2 s-1). The arrows are associated to the convective heat flux: the dimensions of each arrow are scaled with the magnitude of the convective heat flux associated to its ycoordinates: higher are velocities of the fluid, greater are the associated convective heat fluxes. After having provided some insights of the ACR cycle simulations, we want to present the map of the energy performances of the caloric heat pump under investigation. Figure 5 reports the temperature spans vs fluid 15

mass flux evaluated for the heat pump working with the materials introduced in section 3.1. As done in section 3.1, the materials are divided in three groups: electrocaloric and magnetocaloric materials in Figure 5(a); mechanocaloric materials (group 1) in Figure 5(b) and mechanocaloric materials (group 2) in Figure 5(c). Globally, two are the cases investigated that exceed 30 K as temperature span: considering [298; 278] K as indoor-outdoor temperature range, the electrocaloric Pb0.97La0.02(Zr0.75Sn0.18Ti0.07)O3 provides temperature spans between [29.2; 31.3] K under ∆E = 90 MV m-1, whereas the elastocaloric Ni-Ti touches a maximum of 30.7 K for 150 kg m-2 s-1as fluid mass flux and 0.9 GPa as stress-field change. Promising are also the temperature spans given by the barocaloric elastomers acetoxy silicone rubber (from 27.3 K to 28.8 K) if subjected to a pressure field of 0.390 GPa, as well as the ones proper of MnCoGe0.99In0.01 (with a middle value of 27.3 K under ∆p = 0.3 GPa) and of Pb0.97La0.02(Zr0.75Sn0.18Ti0.07)O3 for ∆E =70 MV m-1 with a maximum of 28.2 K. On the other side, much more reduced are the results provided by the electrocaloric Pb0.8Ba0.2ZrO3, the barocaloric (NH4)2MoO2F4 and Vulcanized Natural Rubber that do not exceed 25 K with minimum of 20.7 K touched by VNR, under ∆p = 0.173 GPa and Gf = 250 kg m-2 s-1, as well as the ones of gadolinium that do not exceed 21.1 K. Similar considerations are extendable also to the evaluated heating powers that are shown with respect to fluid mass flux in Figure 6 for: (a) electrocaloric and magnetocaloric, (b) mechanocaloric (group 1), (c) mechanocaloric (group 2) materials. As happened for temperature spans, the highest powers of the investigated caloric heating pump are associated to Pb0.97La0.02(Zr0.75Sn0.18Ti0.07)O3 (∆E = 90 MV m-1) for the electrocaloric group, to Ni-Ti (∆σ = 0.9 GPa) among mechanocaloric, and to ASR (∆p = 0.390 GPa) once again. The maximum heating powers collected in these three cases go from 400 to 600 W. Such results are to be deemed satisfactory if we consider that the power evaluated are referred to a caloric heat pump working with a single ACR regenerator; therefore, solutions mounting multiple Active Caloric Regenerator working parallelly could be adopted in order to enhance the heating power of the pump, with reference to the specific application. On the contrary, all the materials providing powers less or equal to 200 W are not employable for heat pump applications because even the use of advanced design solutions would not be enough to collect adequate powers for real cases. Figure 7 exhibits the coefficients of performance calculated for the: (a) electrocaloric and magnetocaloric, (b) mechanocaloric (group 1), (c) mechanocaloric (group 2) materials and reported with respect to heat transfer fluid mass flux. Furthermore, in Figures 8(a) (b)(c) we report the coefficients of performance also with respect of Carnot COP, as a function of fluid mass flux. The main consideration that arises from Figure 7(a) is that, even if Pb0.97La0.02(Zr0.75Sn0.18Ti0.07)O3 is promising in terms of ∆Tspan and ̇ , the huge work required for operating under such field variation, results in consistent electrical powers that knock down the coefficients of performance of such material that do not exceed 4.7. The related comparison with COPICM sees this material not exceeding 32% of Carnot COP. Gadolinium does not exceed 3 (20% COP/COPICM) but its values are comparable to the ones of Pb0.8Ba0.2ZrO3 at 40.8 MV m-1 even if Gd shows heating powers much smaller than Pb0.8Ba0.2ZrO3. With 16

reference to both groups of mechanocaloric materials, the trends are much more promising (Figures 7(b) and (c)) since NiTi and MnCoGe0.99In0.01 provide really good COPs at least double than the maximum electrocaloric one (60 ~ 80% COPICM), as well as the Acetoxy Silicone rubber, whose COPs are 70 ~ 80 % greater than the ones of Pb0.97La0.02(Zr0.75Sn0.18Ti0.07)O3 and the values of COP/COPICM up to 40 ~ 60%. Such data are to be attributed to smaller mechanical powers needed to vary the external fields applied for making caloric effects manifesting.

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Figure 5. ∆Tspan vs mass flux for: (a) electrocaloric and magnetocaloric, (b) mechanocaloric (group 1), (c) mechanocaloric (group 2) materials.

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20

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Figure 6. ̇ vs mass flux for: (a) electrocaloric and magnetocaloric, (b) mechanocaloric (group 1), (c) mechanocaloric (group 2) materials.

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23

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Figure 7. Coefficient of performances vs mass flux of the active caloric regenerator working with different caloric materials. The materials are divided as: (a) electrocaloric and magnetocaloric; (b) mechanocaloric (group 1); (c) mechanocaloric (group 2).

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Figure 8. COP on Carnot COP vs fluid mass flux, proper of the active caloric regenerator working with different caloric materials. The materials are divided as: (a) electrocaloric and magnetocaloric; (b) mechanocaloric (group 1); (c) mechanocaloric (group 2). 5. Conclusions In this paper, a map of the energy performances of a caloric heat pump is reported for different caloric effect materials. The system is founded on Active Caloric Regenerative heat pump cycle and the investigation was performed through a 2-Dimensional model solved with finite element method and validated experimentally with a caloric prototype in previous investigations. The strong point of the presented heat pump is the possibility of employing every caloric effect material; therefore, basing on general criteria founded in high caloric effect and low environmental impact, a vast set of caloric refrigerants was chosen. They were divided in three groups and tested with [278; 298] K as outdoor-indoor temperature range, 0.8 s as time period of ACR cycle in the range of heat transfer fluid mass flux of [150; 250] kg s-1m-2. From the investigation we drew the following considerations: (1) basing only on temperature spans and heating powers, the most promising materials are Pb0.97La0.02(Zr0.75Sn0.18Ti0.07)O3 (∆E = 90 MV m-1) for the electrocaloric group, Ni-Ti (∆σ = 0.9 GPa)

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and the barocaloric ASR (∆p = 0.390 GPa), among mechanocaloric since ∆Tspan and

̇

are

comparable and quite the same. (2) The huge electrical work required for varying the desired electrical field results in a high expense of electrical power that affects significantly on the coefficients of performance of the electrocaloric materials, including Pb0.97La0.02(Zr0.75Sn0.18Ti0.07)O3. (3) All the mechanocaloric materials require smaller expense to adiabatically vary the mechanical fields and this implies a smaller

̇

. Such results in good COPs, greater than the electrocaloric ones

because of the comparability of temperature spans and heating power emerged in consideration (1). (4) The vulcanized natural rubber together with gadolinium confers the worst energy performances among the investigated materials. Such barocaloric elastomer (VNR) as well as gadolinium, were taken in consideration because of their remarked ecological and non-toxic nature but they completely disregarded the expectations in terms of energy performances. Following the above considerations, it is necessary to specify that the evaluated and shown energy performances, as current system capacity and coefficients of performance, are set to material-based level and not up to the real system level. Indeed, the present investigation must be considered as a feasibility study to underline which materials (and therefore which effects) are more suitable of heat pumping applications, on equal working conditions. Analysing the above points, we conclude that it is possible to conceive caloric heat pumps among the number of the technologies employed for heat pumps realizing. Specifically, based on the present results and the considerations at points (1) - (4), mechanocaloric seems the most promising one. This is not in contradiction with the conclusions of (Aprea et al., 2018a) because, in the present investigation the operating temperatures and the temperature range are both different compared to (Aprea et al., 2018a). This influences the suitability of different caloric materials for the given application. For example, for heat pumping application, it was not possible to employ the magnetocaloric materials of (Aprea et al., 2018a) since their maximum ∆Tad is smaller than the tested mechanocaloric and electrocaloric ones and their magnetocaloric effect is manifesting in a narrower temperature range. By the way, there are some materials whose caloric characteristics make them suitable both for refrigeration and heat pump operation modes and this is the reason why some of the materials investigated in this paper are common with (Aprea et al., 2018a). Furthermore, in the present paper we provided a focus on the elastomer soft materials with barocaloric properties because they are interesting since they are low cost, easy manufacturing and they present a promising giant barocaloric effect in a temperature range devoted to heat pump operation mode. Therefore, we conclude that, in this investigation, the most suitable caloric effect materials to be employed are the mechanocaloric ones since the collected heating powers with respect to the expense required are satisfying for heat pump applications. Moreover, more performing design solutions that conceive the operation of more ACR regenerators parallelly, could be adopted in order to enhance the heating powers of the pump with reference to the desired requirements. 29

References Aprea, C., Greco, A., Maiorino, A. The use of the first and of the second order phase magnetic transition alloys for an AMR refrigerator at room temperature: a numerical analysis of the energy performances. Energy conversion and management, 70, 40-55, 2013. Aprea, C., Cardillo, G., Greco, A., Maiorino, A., Masselli, C. A comparison between experimental and 2D numerical results of a packed-bed active magnetic regenerator. Applied Thermal Engineering, 90, 376-383, 2015. Aprea, C., Greco, A., Maiorino, A., Masselli, C. A comparison between different materials in an active electrocaloric regenerative cycle with a 2D numerical model. International Journal of Refrigeration, 69, 369-382, 2016a. Aprea, C., Greco, A., Maiorino, A., Masselli, C. The energy performances of a rotary permanent magnet magnetic refrigerator. International journal of refrigeration, 61, 1-11, 2016b. Aprea, C., Cardillo, G., Greco, A., Maiorino, A., Masselli, C. A rotary permanent magnet magnetic refrigerator based on AMR cycle. Applied Thermal Engineering, 101, 699-703, 2016c. Aprea, C., Greco, A., Maiorino, A., An application of the artificial neural network to optimise the energy performances of a magnetic refrigerator. International Journal of Refrigeration, 82, 238-251, 2017. Aprea, C., Greco, A., Maiorino, A., Masselli, C. Solid-state refrigeration: A comparison of the energy performances of caloric materials operating in an active caloric regenerator. Energy, 165, 439-455, 2018a. Aprea, C., Greco, A., Maiorino, A., Masselli, C. Energy performances and numerical investigation of solid-state magnetocaloric materials used as refrigerant in an active magnetic regenerator. Thermal Science and Engineering Progress, 2018b. Bansal, P., Vineyard, E., Abdelaziz, O. Status of not-in-kind refrigeration technologies for household space conditioning, water heating and food refrigeration. International Journal of Sustainable Built Environment, 1(1), 85-101, 2012. Benedict, M. A., Sherif, S. A., Beers, D. G., Schroeder, M. G. Design and performance of a novel magnetocaloric heat pump. Science and Technology for the Built Environment, 22(5), 520-526, 2016. Blumenthal, P., Raatz, A. Classification of electrocaloric cooling device types. EPL (Europhysics Letters), 115(1), 17004, 2016. Brown, J. S., Domanski, P. A. Review of alternative cooling technologies. Applied Thermal Engineering, 64(1-2), 252-262, 2014. Chauhan, A., Patel, S., Vaish, R., Bowen, C. R. A review and analysis of the elasto-caloric effect for solid-state refrigeration devices: Challenges and opportunities. MRS Energy & Sustainability, 2, 2015. Chen, X., Xu, W., Lu, B., Zhang, T., Wang, Q., Zhang, Q. M. Towards electrocaloric heat pump—A relaxor ferroelectric polymer exhibiting large electrocaloric response at low electric field. Applied Physics Letters, 113(11), 113902, 2018. Dan’Kov, S. Y., Tishin, A. M., Pecharsky, V. K., Gschneidner, K. A. Magnetic phase transitions and the magnetothermal properties of gadolinium. Physical Review B, 57(6), 3478, 1998. de Vries, W., & van der Meer, T. H. (2017). Application of Peltier thermal diodes in a magnetocaloric heat pump. Applied Thermal Engineering, 111, 377-386, 2017. Engelbrecht, K., Tušek, J., Eriksen, D., Lei, T., Lee, C. Y., Tušek, J., Pryds, N. A regenerative elastocaloric device: experimental results. Journal of Physics D: Applied Physics, 50(42), 424006, 2017. Fähler, S., Rößler, U. K., Kastner, O., Eckert, J., Eggeler, G., Emmerich, H., Entel P., Müller S., Quandt E. Albe, K. Caloric effects in ferroic materials: new concepts for cooling. Advanced Engineering Materials, 14(1‐2), 10-19, 2012. Goetzler, W., Zogg, R., Young, J., Johnson, C. Energy savings potential and RD&D opportunities for non-vapor-compression HVAC technologies. Navigant Consulting Inc., prepared for US Department of Energy, 2014. Gorev, M. V., Bogdanov, E. V., Flerov, I. N., Kocharova, A. G., & Laptash, N. M. Investigation of thermal expansion, phase diagrams, and barocaloric effect in the (NH 4) 2 WO 2 F 4 and (NH 4) 2 MoO 2 F 4 oxyfluorides. Physics of the Solid State, 52(1), 167-175, 2010. Greco, A. Aprea, C., Maiorino, A., Masselli, C. A review of the state of the art of the solid-state caloric cooling processes at room-temperature before 2019. International Journal of Refrigeration, 106, 66-88, 2019. 30

Heath, E. A. Amendment to the Montreal Protocol on Substances that Deplete the Ozone Layer (Kigali Amendment). International Legal Materials, 56(1), 193-205, 2017. Hull, J. R., Uherka, K. L. Magnetic heat pumps for near-room-temperature applications. Energy, 14(4), 177-185, 1989. Imamura, W., Usuda, E. O., Paixão, L. S., Bom, N. M., Gomes, A. M., Carvalho, A. M. G. Supergiant barocaloric effects in acetoxy silicone rubber around room temperature. arXiv preprint arXiv:1710.01761, 2017. Johra, H., Filonenko, K., Heiselberg, P., Veje, C. T., Dall'Olio, S., Engelbrecht, K., & Bahl, C. R. Active magnetic regenerators implemented as a magnetocaloric heat pump for residential buildings. In Proceedings of Thermag VIII-International Conference on Caloric Cooling (2018), 2018a. Johra, H., Filonenko, K., Heiselberg, P., Veje, C., Lei, T., Dall’Olio, S., Engelbrecht, K. & Bahl, C. Integration of a magnetocaloric heat pump in a low-energy residential building. In Building Simulation (Vol. 11, No. 4, pp. 753-763). Tsinghua University Press, 2018b. Kitanovski, A., Plaznik, U., Tomc, U., & Poredoš, A. Present and future caloric refrigeration and heatpump technologies. International Journal of Refrigeration, 57, 288-298, 2015a. Kitanovski, A., Tušek, J., Tomc, U., Plaznik, U., Ožbolt, M., Poredoš, A. Overview of existing magnetocaloric prototype devices. In Magnetocaloric Energy Conversion (pp. 269-330). Springer, Cham, 2015b. Krašna, M., Klemenčič, E., Kutnjak, Z., Kralj, S. Phase-changing materials for thermal stabilization and thermal transport. Energy, 162, 554-563, 2018. Luo, D., Feng, Y., & Verma, P. Modeling and analysis of an integrated solid state elastocaloric heat pumping system. Energy, 130, 500-514, 2017. Montreal Protocol on substances that deplete the ozone layer, United Nation Environment Program (UN), New York, NY, USA, 1987. Moya, X., Defay, E., Heine, V., Mathur, N. D. Too cool to work. Nature Physics, 11(3), 202, 2015. Ossmer, H., Miyazaki, S., Kohl, M. Elastocaloric heat pumping using a shape memory alloy foil device. In Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS), 2015 Transducers-2015 18th International Conference on (pp. 726-729). IEEE, 2015. Peng, B., Fan, H., Zhang, Q. A giant electrocaloric effect in nanoscale antiferroelectric and ferroelectric phases coexisting in a relaxor Pb0. 8Ba0. 2ZrO3 thin film at room temperature. Advanced Functional Materials, 23(23), 2987-2992, 2013. Plaznik, U., Vrabelj, M., Kutnjak, Z., Malič, B., Rožič, B., Poredoš, A., Kitanovski, A. Numerical modelling and experimental validation of a regenerative electrocaloric cooler. International Journal of Refrigeration, 98, 139–149, 2019. Protocol, Kyoto. "United Nations framework convention on climate change." Kyoto Protocol, Kyoto 19, 1997. Qian, S., Ling, J., Hwang, Y., Radermacher, R., Takeuchi, I. Thermodynamics cycle analysis and numerical modeling of thermoelastic cooling systems. International Journal of Refrigeration, 56, 65-80, 2015. Qian, S., Nasuta, D., Rhoads, A., Wang, Y., Geng, Y., Hwang, Y., Radermacher, R., Takeuchi, I. Not-inkind cooling technologies: A quantitative comparison of refrigerants and system performance. International Journal of refrigeration, 62, 177-192, 2016. Qian, S., Yuan, L., Yu, J., Yan, G. Numerical modeling of an active elastocaloric regenerator refrigerator with phase transformation kinetics and the matching principle for materials selection. Energy, 141, 744756, 2017. Qian, S., Yuan, L., Yu, J., & Yan, G. Variable load control strategy for room-temperature magnetocaloric cooling applications. Energy, 153, 763-775, 2018. Smith, A., Bahl, C. R., Bjørk, R., Engelbrecht, K., Nielsen, K. K., Pryds, N. Materials challenges for high performance magnetocaloric refrigeration devices. Advanced Energy Materials, 2(11), 1288-1318, 2012. Smullin, S. J., Wang, Y., Schwartz, D. E. System optimization of a heat-switch-based electrocaloric heat pump. Applied Physics Letters, 107(9), 093903, 2015. Tušek, J., Engelbrecht, K., Millán‐Solsona, R., Mañosa, L., Vives, E., Mikkelsen, L. P., Pryds, N. The elastocaloric effect: A way to cool efficiently. Advanced Energy Materials, 5(13), 1500361, 2015. Tušek, J., Engelbrecht, K., Eriksen, D., Dall’Olio, S., Tušek, J., Pryds, N. A regenerative elastocaloric heat pump. Nature Energy, 1(10), 16134, 2016. 31

Usuda, E. O., Bom, N. M., & Carvalho, A. M. G. Large barocaloric effects at low pressures in natural rubber. European Polymer Journal, 92, 287-293, 2017. Vuarnoz, D., Kitanovski, A., Diebold, M., Gendre, F., Egolf, P. W. A magnetic heat pump with porous magneto caloric material. physica status solidi c, 4(12), 4552-4555, 2007. Wang, Q., Gao, W., Xie, Z. Highly thermally conductive room‐temperature‐vulcanized silicone rubber and silicone grease. Journal of Applied Polymer Science, 89(9), 2397-2399, 2003. Wu R. R., Bao L. F., Hu F. X., Wu H., Huang Q.Z., Wang J., Dong X.L., Li G. N., Sun J. R., Shen F. R., Zhao T. Y., Zheng X. Q., Wang L. C., Liu Y., Zuo W.L., Zhao Y. Y., Zhang M., Wang X.C., Jin C.Q., Rao G. H., Han X. F., Shen B. G.. Giant barocaloric effect in hexagonal Ni 2 In-type Mn-Co-Ge-In compounds around room temperature. Scientific reports, 5, 18027.l, 2015. Zhao, Y., Hao, X., Zhang, Q. A giant electrocaloric effect of a Pb 0.97 La 0.02 (Zr 0.75 Sn 0.18 Ti 0.07) O 3 antiferroelectric thick film at room temperature. Journal of Materials Chemistry C, 3(8), 1694-1699, 2015. Zimm, C., Boeder, A., Mueller, B., Rule, K., Russek, S.L. The evolution of magnetocaloric heat- pump devices. MRS Bull. 43, 274–279, 2018.

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