3D Simulation of thermal field in the core of supercapacitor

From macrostructure of EDLC (Electrochemical double layer capacitor) it is possible to figure out, that for the heat conduction the volumetric properties of EDLC acts as anisotropic surroundings. This structure is in axial and radial direction of EDLC coil geometrically and physically different. Heat transfer through this structure is therefore different in axial direction against heat transfer in radial direction. At examined thermal model of EDLC, the waveform of axial and radial part of thermal coefficient (heat transfer by conduction) in the dependency on order of turn is designed. The graphical interpretation of results from simulation analysis that has been done in COMSOL environment is shown in second part of this paper. 1. Description of EDLC core Cylinder interpretation of EDLC consists of 4 layers with different material properties, assembled in sandwich structure in this order: • Carbon, Carbon • Extruded aluminum • Carbon, • Separator. Label „n“ as total number of turns in fourlayer structure and set 1, j n ∈ as order of sandwich turn. The diameter of turn is being changed in dependency on order of turn according to next formula: ( ) ( ) 0 1 r j r j w = + − (1) where: r(j) – is internal diameter of turn in „j th“ order, r0 – is diameter of first four-layer structure, w – is width of one turn: (2) 2 S C w w w w = + + Al where, wS – is width of separator layer, wC – is width of carbon layer, wAl – is width of extruded aluminum. The area of bottom turn’s side with „j-th“ order is: ( ) ( ) ( ) ( ) 2 2 1 S j r j r j j n = + − ∈ π 1, (3) Axial part of turn’s thermal resistance with „j-th“ order was computed using next formula: ( ) ( ) ( ) . a a L R j k j S j = , (4) where: L – is height of turn coil (m), ka – thermal conductivity in axial direction (W/m.K) 1 University of Zilina, Univerzitna 1, 01026 Zilina, Slovak Republic, tel.:+421 41 513 1600, [email protected] Separator Extruded Aluminum Fig. 1. Cross–section of EDLC structure S a R S r R _ C L r R Al r R _ C R r R Axial thermal resistance of one turn in four-layer sandwich structure consists of four thermal resistances, which are shown on fig.2, whereby: _ C L a R axial thermal resistance of carbon layer on left side, axial thermal resistance of carbon layer on right side, _ C R a R Al a R axial thermal resistance of extruded aluminum layer, S a R axial thermal resistance of separator layer. For several thermal resistances in axial direction of thermal model shown on fig.2 is valid: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2