Heat Transfer Modeling Within Graphite/PCM Composite Materials For High Temperature Energy Storage

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1 OJE DISOR Heat raner Modelin Within Graphite/PCM Compoite Material For Hih emperature Enery Storae V. Morion, E. Palomo Del Bario, M. Rady Ecotock - Pomona - 31 May 2 June 26

2 Context o the Project DISOR ( European project : 6th Framework Proramme or Reearch ) DSG echnoloy Parabolic trouh collector Partner : -DLR (Germany) -REFLE, IMP (France) -CIEMA (Spain) -WIS (Irael) -CLSE (Bularie) -7 companie Ecotock - Pomona - 31 May 2 June 26

3 Synthetic Graphite Natural Graphite Exoliated Natural Graphite Material Graphite + NO 3 K/NO 3 Na LH 1 kj.k -1 m 223 C SGL Ecotock - Pomona - 31 May 2 June 26

4 heoretical development From the equivalent continuum to the ytem and/or plant cale Heat traner modelin: From the µ-cale to the equivalent continuum 1 mm 2 µm Material tructure: Undertandin and modelin Ecotock - Pomona - 31 May 2 June 26

5 From micro-cale to the equivalent continuum Equivalent continuum Space-time contraint Enery equation Macrocopic phyical propertie Repreentative Volume L - phae raphite S - phae H t Graphite H t ( ) Graphite n Ecotock - Pomona - 31 May 2 June 26

6 Ecotock - Pomona - 31 May 2 June 26 ( ) & n t H t H interace Graphite Graphite Volume averain method Main hypothei : Local thermal equilibrium K t H eq L c c H ε ε ε + + ) ( ( ) + + A eq da b n V I K ) ( ε ε ( ) > < max max min min min 1 1 St ( ) : / : : K n Interace Sel Graphite Sel K Graphite Homoeneou equivalent medium Enthalpy model Solution o the Laplace problem in the elementary cell Phae chane underoe over a temperature rane intead o at determined temperature

7 Material tructure : undertandin and modelin 1 mm 1 µm 1 µm HREE SCALES he ample Collaped worm & Inter particle poroity he elementary heet & Intra particle poroity Ecotock - Pomona - 31 May 2 June 26

8 Reular pavin 1 µm Flattened reular honeycomb network e v e h Elementary cell H h l H l 1 l 2 β e 2 l 1 L Ecotock - Pomona - 31 May 2 June 26 L

9 Axial and radial thermal conductivitie o the ENG matrix hermal conductivity (W.m-1.K-1) Radial Axial Matrix denity (k.m-3) Ecotock - Pomona - 31 May 2 June 26

10 Worm denity o the ENG matrix Worm denity (k.m-3) Matrix denity (k.m-3) Ecotock - Pomona - 31 May 2 June 26

11 ENG matrix peciic urace Speciic urace (m².-1) Matrix denity (k.m-3) Ecotock - Pomona - 31 May 2 June 26

12 otal poroity o the ENG matrix and worm poroity Poroity,98,96,94,92,9,88,86 matrix worm Matrix denity (k.m-3) Ecotock - Pomona - 31 May 2 June 26

13 Meaurement and eective thermal conductivitie hermal conductivity (W.m-1.K-1) Meaured reult Numerical reult Matrix dentity (k.m-3) Ecotock - Pomona - 31 May 2 June 26

14 Validation Can heat traner in ENG/alt media be repreented by mean o homoeneou media? What time-cale contrain mut be veriied or? Phae chane in equivalent ENG/alt homoeneou media look like phae chane o a pure ubtance (harp olid/liquid interace) or like phae chane over a temperature rane (muhy reion development)? Are eective phyical propertie or the equivalent homoeneou medium correctly deined? Ecotock - Pomona - 31 May 2 June 26

15 Ecotock - Pomona - 31 May 2 June 26 Methodoloy ) n Graphite alt t H raphite t H alt t H eq eq Homoeneou medium hermal behavior comparion

16 Meltin in a hal-pace Adiabatic condition Dirichlet condition ( x, y, t) + 1 Homoeneou or Heteroeneou medium ( x, y, t ) ( olid tate ) x Adiabatic condition Exact olution o the problem in a homoeneou medium emperature ( x, t) ( q(, t) er with o ( t) 2ξ Heat lux at x o α t ξ exp( ξ ) er ield x er 2 α t er ( ξ ) ( ξ ) ( ξ ) Meltin ront poition ) o π α t Ste c( 2 o ; π Ste L ) Dimenionle orm emperatur e ( x ( ξ ) ( ξ ) t Ecotock - Pomona - 31 May 2 June 26, t ( t) 2ξ t q (, t) x er 2 t ) er Meltin ront poition Heat lux at x ield π er 1 Similarity variable x q re o x L L re L ( re ; o q t o α t L ) 2 re

17 Sharp interace emperatur e ield µ er 2 ( µ ) er ( ξ ) emperatur e Muhy reion ( µ ) ield µ er 2 Meltin ront ( µ ) 2ξ poition Meltin ront ' ( µ ) 2ξ poition Heat lux at x q (, t ) π er 1 ( ξ ) t Heat lux at x q (, t) π er 1 ' ( ξ ) t Pore-cale model Continuum model Pure ubtance qrt(t) Ecotock - Pomona - 31 May 2 June 26

18 Numerical validation tet Matrix denity (k/m3) Micro poroity Macro poroity Worm imulation Empty Empty Without phae chane With phae chane Matrix imulation Empty Empty Without phae chane Empty Empty With phae chane Ecotock - Pomona - 31 May 2 June 26

19 Reult or a matrix denity o 2 k/m3.9 Dimenionle Continuum model Pure ubtance Pore-cale model raphite-alt ( C) t 5 t Similarity variable x (-) Heat lux at x (W) Pore-cale model Continuum model Pure ubtance (-) Continuum model Pure ubtance Pore-cale model Ecotock - Pomona - 31 May 2 June qrt(t)

20 Reult or a matrix denity o 2 k/m3 Phae chane D ( C) : 1.1 Dimenionle temperature Dimenionle ERF(Similarity variable) ERF (Similarity Variable) Ecotock - Pomona - 31 May 2 June 26

21 Concluion Heat traner in G/S matrix can be repreented by equivalent homoeneou model at the time cale o interet Equivalent thermal capacity and latent heat in the homoeneou model can be obtained by imple weihtin o the phae (G/S) propertie. Equivalent thermal conductivitie (axial & radial) are deined by a imple Laplace problem. Such deinition i in coherence with uual macrocopic meaurement. he enthalpy-temperature unction mut be modiied. At the macrocopic cale the phae chane in the G/S matrix behave like a phae chane problem over a temperature rane. Future work Empirical validation Ecotock - Pomona - 31 May 2 June 26