Solidification heat transfer characteristics of nanoparticle-enhanced phase change material inside rectangular slabs

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International Conference On Materials And Energy 2015, ICOME 15, 19-22 May 2015, Tetouan, Morocco, and the International Conference On Materials And Energy 2016, ICOME 16, 17-20 May 2016, La Rochelle, France The 15th International Symposium on District Heating and Cooling

Solidification heat transfer characteristics of nanoparticle-enhanced Assessing feasibility of using heat demand-outdoor phasethe change material insidethe rectangular slabs temperature function for district heat demand forecast a a long-term a, b a

Radouane Elbahjaoui , Hamid El Qarnia *, Mohammed El Ganaoui a,b,c a a b c c I. University, AndrićFaculty *,ofA. PinaSemlalia, , P. Ferrão , J. Fournier B. Lacarrière , O. URAC Le Corre Cadi Ayyad Sciences Fluids Mechanic and Energetic ., Laborator (Affiliate to CNRST, 27) Department of a

Physics, P.O. 2390, Marrakesh, Morocco IN+ Center for Innovation, bTechnology and Policy Research - Instituto Superior Técnico, Av.Nancy, Rovisco Pais 1, 1049-001 Lisbon, Portugal University of Lorraine, LERMAB/IUT Longwy, Institut Carnot, France b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France

Abstract Abstract This paper presents a numerical investigation on the heat transfer enhancement during solidification of a phase change material in a rectangular latent heat storage unit (LHSU) through the dispersion of high conductive nanoparticles. The storage unit consists District heating networks oriented are commonly in the literaturephase as one of thematerial most effective solutions the of a number of vertically slabs ofaddressed nanoparticle-enhanced change (NEPCM) placed for in adecreasing laminar heat greenhouse emissions building sector. Thesemodel systems high investments which are returned heat transfer fluidgas (HTF) flow. from A twothedimensional numerical hasrequire been developed using the enthalpy methodthrough and thethefinite sales. Due to thetochanged climate conditions and and building renovation policies, demand in theprocess. future could decrease, volume approach investigate the thermal behavior performance of the LHSUheat during discharging The numerical prolonging the investment return period. model has been validated by comparing our numerical predictions with the experimental and numerical results published in The main Numerical scope of this paper is towere assess the feasibility of usingthe theeffect heat demand – outdoor fraction temperature function for heat demand literature. simulations carried out to evaluate of the volumetric of nanoparticles on the heat forecast.enhancement The districtand of storage Alvalade, located inofLisbon (Portugal), transfer performance the storage unit. was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were resultsPublished from a dynamic heat Ltd. demand model, previously developed and validated by the authors. ©compared 2017 Thewith Authors. by Elsevier The results showed that when only weather change is considered, the margin of ICOME error could be acceptable for some applications Peer-review under responsibility of the scientific committee of ICOME 2015 and 2016. (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios,solidification; the error value up to (PCM) 59.5% ;(depending weather and renovation scenarios combination Keywords: Phaseincreased change material heat transfer on fluidthe (HTF); nanoparticles; latent heat storage unit (LHSU) considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +212-666-350-016; fax: +212-524-436-769. Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected] 1876-6102 © 2017 The Authors. Published by Elsevier Ltd.

Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.

1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of ICOME 2015 and ICOME 2016 10.1016/j.egypro.2017.11.258

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1. Introduction Latent heat storage systems using phase change materials (PCMs) are considered the most preferable methods for storing produced solar thermal energy and extending the operational time of thermal systems. These systems have high storage capacity and isothermal behavior during charging and discharging processes. However, the thermal conductivity of PCMs is generally low and limits the charging and discharging rates. To overcome this drawback, several techniques have been suggested in the literature including the dispersion of high conductive nanoparticles, use of multiple PCMs, and integration of metal matrix in PCMs. Among these techniques, the dispersion of nanoparticles is considered as a new promising technology and it is adopted in the present study. Nomenclature cp d f h H k

specific heat at constant pressure (J/kg K) NEPCM slabs thickness (m) liquid fraction specific enthalpy (J/ kg) height of the NEPCM slabs (m) thermal conductivity (W/m K) ɺ m mass flow rate of HTF (kg/s) Nc number of HTF channels p pressure (Pa) T temperature (K) t time (s) u,v velocity components (m/s) w thickness of HTF channels (m) x, y cartesian coordinates (m) Greek symbols α thermal diffusivity (m2/s)

ϕ volumetric fraction of nanoparticles β coefficient of expansion (K-1) µ dynamic viscosity (Ns/m3) ν kinematic viscosity (m2/s) ∆h latent heat (J/kg) ρ density (kg/m3) ψ stream function (m2/s) Ψ dimensionless stream function (=ψ/ αm,l) Subscripts e inlet m PCM melt melting nm NEPCM f fluid l liquid s solid

In the previous numerical studies on the melting and solidification of PCM in rectangular slabs separated by rectangular channels in which circulates heat transfer fluid (HTF) [1-7], the effect of natural convection was not taken into account. Such an assumption is only valid when the PCM slabs are horizontally oriented as reported by Laouadi and Lacroix [8]. Furthermore, only a base PCM is filled in these storage units which delays the time of charging and discharging processes. In the present study, the solidification of base PCM (n-octadecane) dispersed with high conductive nanoparticles (copper) is numerically investigated. The slabs filled with NEPCM are vertically oriented and the effect of natural convection is taken into consideration by resolving the momentum equations containing the buoyancy term. The developed two-dimensional numerical model was validated by experimental and numerical results found in literature. Thereafter, the numerical simulations were conducted to evaluate the effect of the volumetric fraction of nanoparticles on the thermal behavior and performance of the storage unit. 2. Governing equations and validation 2.1. Storage unit description The storage unit under investigation is presented in Fig. 1. It is composed of a number of identical slabs initially filled with superheated NEPCM. The initial temperature of the superheated liquid NEPCM is Ti = 311.33 K. A cold heat transfer fluid flows between the slabs and extracts heat from NEPCM which begins to solidify. The inlet temperature and the mass flow rate of HTF circulating in the storage unit are taken constant at values 280.33 K and 0.116 kg/s, respectively. The thickness of the HTF channels, w , height of the latent heat storage unit (LHSU), H , half width of the NEPCM slabs, d / 2 , and number of HTF channels, N c , are 0.6 cm, 17.3 cm, 2.88 cm and 10,

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respectively. For considerations of symmetry, the analysis of the whole LHSU can reduced to the study of a repetitive volume composed of half a HTF channel and half a NEPCM slab as shown in Fig. 2. 2.2. Mathematical formulation A two-dimensional mathematical model has been developed for both NEPCM and HTF. The HTF and liquid NEPCM are incompressible and Newtonian, and their flows are laminar. The HTF flow is assumed hydrodynamically developed. The HTF, PCM and nanoparticles used in numerical calculations are water, n-octadecane and copper nanoparticles, respectively. Their thermo-physical properties are displayed in Table 1.

Fig.1 Schematic of the latent heat storage unit (LHSU)

Fig.2 Computational domain

Using the enthalpy method to mathematically formulate the phase change, the governing equations are given as follows: For HTF ∂Tf ∂(vf Tf ) ∂ ∂T ∂T ∂ (α f f ) + (α f f ) + = (1) ∂t ∂y ∂x ∂x ∂y ∂y where v f =

3 x 2 Vmoy (1 − ( ) ) 2 w/2

(2)

For NEPCM

∂ (ρnm u) ∂ (ρnm v) + =0 ∂x ∂y

(3)

∂(ρnm u) ∂(ρnm uu) ∂(ρnm vu) (1 − f )2 ∂p ∂ ∂u ∂ ∂u u nm + + = − + (µnm ) + (µnm ) − C 3 (f + b) ∂t ∂x ∂y ∂x ∂x ∂x ∂y ∂y

(4a)

∂(ρnm v) ∂(ρnm uv) ∂(ρnm vv) (1 − f )2 ∂p ∂ ∂v ∂ ∂v vnm + ρnm gβnm (Tnm − Tmelt ) + + = − + (µnm ) + (µnm ) − C 3 (f + b) ∂t ∂x ∂y ∂y ∂x ∂x ∂y ∂y

(4b)

∂(ρnm h) ∂(ρnm uh) ∂(ρnm vh) ∂ k nm ∂h ∂ k ∂h ∂f ) + ( nm ) − ρm ∆h nm + + = ( (5) ∂t ∂x ∂y ∂x cp,nm ∂x ∂y cp,nm ∂y ∂t The density, specific heat, Boussinesq term, latent heat, dynamic viscosity and thermal conductivity of the NEPCM are expressed as follows:

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ρnm = φρn + (1 − φ ) ρm , (ρc p )nm = φ ( ρc p )n + (1 − φ )( ρc p )m , ( ρβ )nm = (1 − φ )( ρβ )m + φ ( ρβ )n , (ρ∆h)nm = (1 − φ )( ρ∆h)m , µnm =

k + 2km − 2(km − kn )φ µm km , kd = C ∗ ( ρ c p )nm u 2 + v 2 dn and knm = keff + kd , . , keff = n 2.5 kn + 2km + (km − kn )φ (1 − φ )

where keff represents the thermal conductivity of the stagnant NEPCM, kd is the thermal conductivity enhancement term which is due to the Brownian motion, dn is the diameter of the nanoparticles (dn=45 nm) and C* is an empirical constant (C* = 0.1). The initial and boundary conditions of the investigated LHSU are given as follows:

t =0

Tf = Tnm = Ti , u = v = 0

∂Tf =0 ∂x ∂T ∂T x = w / 2 k f f = k nm nm , u = v = 0 ∂x ∂x ∂Tnm y = 0 Tf = Te , = 0, u = v = 0 ∂y x=0

x = w / 2+d/ 2

∂Tnm ∂v = 0, u = 0, =0 ∂y ∂x

(6a) (6b) (6c) (6d) (6e)

∂Tf ∂Tnm (6f) = = 0, u = v = 0 ∂y ∂y The numerical model has been implemented in a self-developed FORTRAN code based on the finite volume method. The power law scheme has been used to treat the convection terms in governing equations and the SIMPLE algorithm has been adopted to approximate the pressure-velocity coupling. Before carrying out the numerical simulations, the developed numerical model has been first validated by comparing our numerical predictions with the experimental data obtained by Gau and Viskanta [9] and the numerical results of Brent et al. [10] and Khodadadi and Hosseinizadeh [11] for the melting of Gallium as PCM in a differentially heated cavity. The results are given in term of melting front position as shown in Fig. 3. The developed numerical model has been also compared with the numerical results of Khodadadi and Hosseinizadeh [11] for the solidification of water dispersed with nanoparticles in a differentially heated cavity. The results are presented in term of time-wise variation of the liquid fraction as illustrated in Fig. 4. The analysis of these results shows that a good agreement exists between our numerical predictions and the experimental and numerical results published in literature. y=H

3. Results and discussions The liquid fraction contours and the structure of the liquid NEPCM flow at times: t = 30.83 min, 95.16 min, 141.83 min and 340.33 min are illustrated in Figs. 5 and 6 for ϕ = 0% and 8%, respectively. In the early stage, the solid-liquid interface develops close to the heat exchange wall separating HTF and NEPCM. Its shape appears substantially planar in the bottom part of the NEPCM slab and slightly curved in the upper part. This behaviour is mainly due to the natural convection movement which transports hot liquid NEPCM to the upper part of the slab and delays the solidification rate in this section. As time progresses, the solid-liquid interface moves progressively to the right side of the slab and the natural convection flow gradually decreases. It is worth noting that the solid-liquid interface moves faster in the right side and the solidification rate increases with increasing volumetric fraction of nanoparticles (ϕ = 8%). The time-wise variations of the total sensible and latent heats discharged from NEPCM for several nanoparticles’ volumetric fractions are shown in Figs. 7 and 8, respectively. In the early stage, the thermal energy is discharged from NEPCM by sensible heat. Therefore, the sensible total heat undergoes a rapid increase due to the natural convection impact and to the high initial temperature of the liquid NEPCM. As time goes on, the solidification process begins to take place and the slope of the sensible heat curves decreases. Furthermore, the total latent heat

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discharged undergoes a non-linear increase to reach its maximum value. It is worth noting that the increase of the volumetric fraction of nanoparticles leads to the increase in the maximum value of the total sensible heat and to the decrease in the maximum value of the latent heat discharged. This is explained by the fact that the principle of dispersion of nanoparticles is based to the replacement of a volumetric fraction of base PCM by nanoparticles. 1 0.06 2 min

0.9

17 min

0.7

6 min 10 min

Liquid fraction

y (m)

0.04

0.03

0.02

0.6 0.5 0.4 0.3 0.2

Current model Brent at al. Khodadadi and Hosseinizadeh Gau and Viskanta

0.01

0

Current model φ = 0% Current model φ = 10% Current model φ = 20% Khodadadi and Hosseinizadeh φ = 0% Khodadadi and Hosseinizadeh φ = 10% Khodadadi and Hosseinizadeh φ = 20%

0.8

0.05

0

0.01

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0.05

0.06

0.07

0.1 0

0.08

0

500

1000

1500

2000

2500

3000

Time (s)

x (m)

Fig. 3 Comparison of the melting front positions of the current model with those obtained by other numerical and experimental studies

Fig. 4 Comparison of the time-wise variation of the liquid fraction obtained by the current model and that of the numerical study of Khodadadi and Hosseinizadeh [11]

Table 1. Thermal properties of HTF, PCM and copper nanoparticles Property

HTF(water)

n-octadecane

Copper nanoparticles

Density (kg/m )

989

774.5

8954

Specific heat (J/kg/K)

4180

2225

383

Thermal conductivity (W/m K)

0.64

0.1505

3

(a)

φ = 0% t = 30.83 min

0.16

(b)

-6

400 -3

Dynamic viscosity (kg/m s)

577x10

Latent heat (kJ/kg)

-

Thermal expansion (1/K)

-

9.42 x10

Melting temperature (K)

-

301.33

φ = 0% t = 95.16 min

0.16

(c)

φ = 0% t = 141.83 min

0.16

(a) f

0.16

0.12

0.12

0.1

0.1

0.1

0.1

(c)

φ = 8% t = 141.83 min

φ = 8% t = 340.33 min

(d)

0.16

0.16

0.16

0.16

0.14

0.14

0.14

0.14

0.12

0.12

0.12

0.12

0.1

0.1

0.1

0.1

0.08

0.08

0.08

0.08

0.08

0.08

0.08

0.06

0.06

0.06

0.06

0.06

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0.02

0.02

0

0.01

0.02

x

0.03

0

0.01

0.02

x

0.03

0

0.01

0.02

x

0.03

0

0.01

0.02

x

0.03

Fig. 5 Instantaneous variation of the liquid fraction contours for φ = 0%.

0

0.01

0.02

x

0.03

0

0.01

0.02

x

0.03

f 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

y

0.08

y

y

0.12

φ = 8% t = 95.16 min

y

0.12

(b)

y

0.14

-

φ = 8% t = 30.83 min

y

0.14

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

1.67x10-5

y

0.14

-4

y

0.14

-

270.159

φ = 0% t = 340.33 min

(d)

3.57x10

0

0.01

0.02

x

0.03

0

0.01

0.02

x

Fig. 6 Instantaneous variation of the liquid fraction contours for φ = 8%.

0.03

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6 1.1 x 10

6 0.3 x 10

1 0.25

0.9

Total latent heat (J)

Total sensible heat (J)

0.8 0.2

0.15

0.1

φ = 0% φ = 2% φ = 8%

0.7 0.6

φ = 0% φ = 2% φ = 8%

0.5 0.4 0.3 0.2

0.05

0.1 0

0

100

200

300

400

500

600

700

800

Time ( min )

Fig. 7 Time-wise variation of the total sensible heat discharged from NEPCM 4. Conclusion

0

0

100

200

300

Time ( min )

400

500

600

Fig. 8 Time-wise variation of the total latent heat discharged from NEPCM

The solidification of nanoparticle-enhanced phase change material in a rectangular LHSU is numerically investigated. A two-dimensional model has been developed and validated by experimental and numerical results found in the literature. The effect of the volumetric fraction of nanoparticles on the thermal performance enhancement of the storage unit is numerically evaluated. The results show that the dispersion of nanoparticles enhances the heat transfer and improves the solidification rate of NEPCM. References [1] Charvát P, Klimeš L, Ostrý M, Numerical and experimental investigation of a PCM-based thermal storage unit for solar air systems. Energy and Buildings 2014; 68, Part A: 488-497. [2] Bechiri M, Mansouri K, Exact solution of thermal energy storage system using PCM flat slabs configuration. Energy Conversion and Management 2013; 76: 588-598. [3] Osterman E, Butala V, Stritih U, PCM thermal storage system for ‘free’ heating and cooling of buildings. Energy and Buildings 2015; 106: 125-133. [4] Mosaffa A H, Infante Ferreira C A, Rosen M A, Talati F, Thermal performance optimization of free cooling systems using enhanced latent heat thermal storage unit. Applied Thermal Engineering 2013; 59: 473-479. [5] Lopez J P A, Kuznik F, Baillis D, Virgone J, Numerical modeling and experimental validation of a PCM to air heat exchanger. Energy and Buildings 2013; 64: 415-422. [6] Liu M, Belusko M, Steven Tay N H, Bruno F, Impact of the heat transfer fluid in a flat plate phase change thermal storage unit for concentrated solar tower plants. Solar Energy 2014; 101: 220-231. [7] El Qarnia H, Theoretical study of transient response of a rectangular latent heat thermal energy storage system with conjugate forced convection. Energy Conversion and Management 2004; 45: 1537-1551. [8] Laouadi A, Lacroix M, Thermal performance of a latent heat energy storage ventilated panel for electric load management. International Journal of Heat and Mass Transfer 1999; 42: 275-286. [9] Gau C, Viskanta R, Melting and solidification of a metal system in a rectangular cavity. International Journal of Heat and Mass Transfer 1984; 27: 113-123. [10] Brent A D, Voller V R, Reid K J, Enthalpy-porosity technique for modeling convection-diffusion phase change: Application to the melting of a pure metal. Numerical Heat Transfer 1988; 13: 297-318. [11] Khodadadi J M, Hosseinizadeh S F, Nanoparticle-enhanced phase change materials (NEPCM) with great potential for improved thermal energy storage. International Communications in Heat and Mass Transfer 2007; 34: 534-543.