Farid Samara 1, Dominic Groulx 1 and Pascal H. Biwole 2 1

Transcription

1 Farid Saara 1, Doinic Groulx 1 and Pascal H. Biwole 2 1 Departent of Mechanical Engineering, Dalhousie University 2 Departent of Matheatics and Interactions, Université of Nice Sophia-Antipolis Excerpt fro the Proceedings of the 2012 COMSOL Conference in Boston

2 Sensible Heat Storage: A heat storage syste that uses a heat storage ediu, and where the addition or reoval of heat results in a change in teperature herocheical Storage: Storage of energy is the result of a cheical reaction Latent Heat Storage: he storage of energy is the result of the phase change (solidliquid or solid-solid) of a phase change aterial (PCM). he process happening over a sall teperature range.

3 PV Panel Unfortunately, the efficient of solar PV decreases with an increase in teperature! PCM can be use to absorb the extra energy during the day, keeping the PV at a lower, ore efficient, teperature.

4 2D Convection Doinated

5 H = L = 0.02 Aluinu thickness l = he entire PCM is initially solid at roo teperature, o = 293 K. At t = 0, q = 1000 W/ 2 Forced convection: ( = o ) Left wall: h = 10 W/ 2 K right wall: h = 5 W/ 2 K Biwole, P., P. Eclache, and F. Kuznik, Iproving the Perforance of Solar Panels by the use of Phase- Change Materials, World Renewable Energy Congress 2011, Linköping, Sweden, 8 p. (2011)

6 he phase change aterial used in this coparison study is R25 Cp (J/kg K) k (W/ K) ρ (kg/ 3 ) Solid R Liquid R Aluinu Other Properties of R25 L F = J/Kg β = /K = K μ = kg/ s

7 1 st Method: Modified Viscosity 2 nd Method: Modified Volue Force

8 Proble type: ransient theral fluid* Model used: Lainar Flow Heat ransfer in a Liquid ransient Analysis hese odels encopass: Lainar flow driven by the body force Heat transfer by conduction and convection 2D Geoetry Over the entire doain Modified using the Effective Heat Capacity Method and a properly defined viscosity over the entire teperature range. * he treatent of phase change renders the proble non-linear as well.

9 C p { C p, s C p, C p, l 303 K 313 K K K C C p, s p, l = Solid phase C P = 1.8 kj/kg = Liquid phase C P = 1.8 kj/kg Where Cp, C p, s C 2 p, l L f L = Latent heat of fusion = 232 kj/kg = Melting eperature range = 1 K

10 Nuerically, the odified C p is incorporated in COMSOL using the piecewise function in the aterial properties. A continuous second derivative is used.

11 he dynaic viscosity, was input as a piecewise, continuous, second derivative function centered about +Δ/2. () 6 10, l, x x / 2 / 2 It accounted for the viscosity of the liquid PCM in the elted region and forced the solid PCM to reain fixed by having a solid viscosity of 10 6

12 2 ) ( 2 2 () e D ) ( 1, ) ( ) (, 2 ) ( 0, () B

13 C p C p, s ( C p, l C ) B( ) p, s LD( ) C C p, s p, l = Solid phase C P = 1.8 kj/kg = Liquid phase C P = 1.8 kj/kg L = Latent heat of fusion = 232 kj/kg = Melting eperature range = 1 K

14 () l 1 A( ) with 2 C(1 B( )) A( ) 3 ( B( ) q) where C and q are arbitrary constants C = 10 5 q = 10-3

15 Both ethods use the Boussinesq approxiation to account for the buoyancy forces in the elted PCM. his force is added into the odel via the voluetric force in the fluid physics interface: F b g l ( )

16 u 2 t with F a u u u P F F b a A( ) u F he ipact of a is to doinate every other force ters in the oentu equations when the PCM is solid, speeding up the calculation and effectively forcing a trivial solution of u = 0 in the solid.

17 2D quadrilateral eleents; 9200 or eleents were selected (any ore eleents required siulation longer than a week!); Both linear and quadratic eleents where used. Siulations took an average of 5 to 7 days to run in a Xeon QuadCore.

18 2D free triangular eleents; eleents were selected; Only linear eleents where used. Siulations took an average of 5 to 7 days to run in a Xeon QuadCore.

19 Coparison

20 Model Nuber Brief Description eperature Discretization Nuber of Eleents Mesh Geoetry Boundary Layer otal elting tie Nuber of iterations Length of the Siulation 1 1 st Method Linear Free riangular Around the inner wall Diverged at 4200 sec 2 2 nd Method Linear Free riangular Around the inner wall 6060 sec hours 3 2 nd Method Quadratic nd Method Linear by 30 quadrilateral 200 by 30 quadrilateral On the left wall On the left wall 7380 sec hours 7560 sec (MF=96 %) hours 5 2 nd Method (F a = 0) Linear Free riangular Around the inner wall 6000 sec hours 6 2 nd Method Quadratic by 45 quadrilateral Around the inner wall 6630 sec hours

21 Pipe eperature Profile Model 2 Model 6

22 Pipe Velocity Profile Model 2 Model 6

23 he physical processes encountered during transient phase change heat transfer, coupled with conduction and convection, in a PCM can be odeled nuerically using COMSOL Multiphysics; Between the two ethods presented, the second, having a ore thorough atheatical treatent, with better defined functions, specific heat, viscosity and volue force in the Navier-Stokes equation, provides a ore robust ethod; However, the effect of the esh, and soe extra ters incorporated with the 2 nd ethod are still not clearly understood and will require experiental work to clearly be understood.