Modelling a packed-bed latent heat thermal energy storage unit and studying its performance using different paraffins

Figures & data

Figure 1. Temperature–time diagram for the heating of a substance (Regin, Solanki, and Saini 2008).

Table 1. Typical materials used in sensible heat TES systems (Cabeza et al. 2015).

Material	Density $(\mathrm{kg}/{\mathrm{m}}^3)$	Specific heat $\left(\mathrm{J}/\mathrm{kg}\mathrm{K}\right)$	Volumetric thermal capacity $\left(10^6\mathrm{J}/{\mathrm{m}}^3\mathrm{K}\right)$
Clay	1,458	879	1.28
Brick	1,800	837	1.51
Sandstone	2,200	712	1.57
Wood	700	2,390	1.67
Water	988	4,182	4.17

Table 2. Typical materials used in latent heat TES storage (Cabeza et al. 2015).

Material	Melting temperature (°C)	Melting Enthalpy $(\mathrm{MJ}/{\mathrm{m}}^3)$
Water-salt solutions	−100 to 0	200–300
Water	0	330
Clathrates	−50 to 0	200–300
Paraffins	−20 to 100	150–250
Salt hydrates	−20 to 80	200–600

Figure 2. Classification of PCMs.

Table 3. Physical properties of some paraffins (Sharma et al. 2009).

Paraffin	Freezing point/range (°C)	Heat of fusion (kJ/kg)
6106	42–44	189
P116^c	45–48	210
5838	48–50	189
6035	58–60	189
6403	62–64	189
6499	66–68	189

Table 4. Physical properties of some non-paraffins (Sharma et al. 2009).

Non-paraffins	Melting point (°C)	Latent heat (kJ/kg)
Formic acid	7.8	247
Phenol	41	120
Thymol	51.5	115
Acrylic acid	68	115
Benzoic acid	121.7	142.8

Figure 3. Typical geometries of PCM containers (Agyenim et al. 2010).

Figure 4. Different containment schematics used in LHTS systems (Regin, Solanki, and Saini 2008): (a) flat plate; (b) shell and tube with internal flow; (c) shell and tube with parallel flow; (d) shell and tube with cross flow; (e) sphere packed bed.

Figure 5. (a) Schematic of a PCM bed TES tank with spherical capsules, (b) HTF flow around PCM (He et al. 2022).

Figure 6. The TES system operation modes (He et al. 2022).

Figure 7. Shell-and-tube unit (Trp 2005).

Figure 8. Module arrangement of PCM containment (Zeinelabdein, Omer, and Gan 2018).

Figure 9. Effect of inlet temperature on the (a) total melting time and (b) solidification time (Avci and Yazici 2013).

Figure 10. Schematic of experimental setup (Nallusamy, Sampath, and Velraj 2006).

Table 5. Main outcomes for each material.

Types of paraffin	Main outcomes
Technical grade paraffin RT30	Well-suited for heat storage, aids in TES unit optimisation, and provides insight into PCM behaviour.
Paraffin RT28HC	Module setup impacts effectiveness, TES improvement possible with optimised PCM panel distance, wider air channels can regulate the melting process.
Paraffin wax	Efficiency confirmed, tube diameter plays a major role in performance, aids in LHTES system design.
Paraffin RT 58	Enhanced heat transfer when used in metal foam, inlet conditions crucial.
Paraffin of P56-58 (MERCK)	Asymmetrical convection impacts melt patterns and phase change speed, enabling novel designs.

Figure 11. 2D model geometry.

Figure 12. 3D model geometry.

Figure 13. Boundary conditions.

Table 6. Specification of the TES tank.

Parameter	Value
Diameter of encapsulated PCM (spherical pellets) (m)	0.055
Bed porosity	0.49
Flow rate (kg/min)	2
Initial temperature (°C)	25
Solar heating power (W)	375
Volume of storage tank (m^3)	0.048
Volume of PCM in the spherical capsules (m^3)	0.024
Volume of water in the storage tank	0.023
No. of spherical capsules of 55 mm diameter	264
Mass of spherical capsules (kg)	4.00

Figure 14. Mesh configuration.

Table 7. Material selection.

Material	Selection
Water, liquid	Domains 1,2, 3
Paraffin, solid/liquid	Domain 2
Glass Wool	Domain 4

Table 8. Mesh statistics.

Number of elements	Triangles	Quads	Edge elements	Vertex elements
7728	7131	597	496	28

Figure 15. (a) HTF Temperature, (b) PCM Temperature (Nallusamy, Sampath, and Velraj 2006).

Figure 16. COMSOL results. PCM and HTF temperature distribution.

Figure 17. COMSOL results. PCM & HTF temperatures of TES tank using RT30.

Figure 18. COMSOL results. PCM & HTF temperatures of TES tank using RT28HC.

Figure 19. COMSOL results. PCM & HTF temperatures of TES tank using WAX.

Figure 20. COMSOL results. PCM & HTF temperatures of TES tank using RT58.

Figure 21. COMSOL results. PCM & HTF temperatures of TES tank using P56-58.

Figure 22. COMSOL results. The effect of varying porosity.

Figure 23. COMSOL results. The effect of varying the HTF flow rate.

Table 9. Charging characteristics of the PCMs.

Paraffin	RT30	RT28HC	Wax	RT58	P56-58
Max. Charging Temperature (K)	307	308	339	339	337
Temperature difference $\mathrm{\Delta T}$ (K)	9	10	41	41	39
Time required for the charging process (h)	4.2	4.8	8.6	9.7	10

Table 10. Thermophysical properties of the different paraffins.

Property	Reference	RT30	RT28HC	Wax	RT 58	P56-58
Phase change temperature (K)	333	300.7	301	334	333	331.6
Latent heat (kJ/kg)	213	206	250	190	181	250
Thermal conductivity
(W/m K) – solid/liquid	0.4/0.15	0.18/0.19	0.2 / 0.2	0.24 / 0.22	0.2	0.21/0.2
Heat capacity of PCM
(J/g K) – solid/liquid	1.85/2.28	1.8/2.4	2 / 2	2 / 2.15	2.1/2.2	1.84 / 2.37
Density (kg/m^3) – solid/liquid	861/778	789/750	880 / 770	910/790	840	820/780

Table 11. Heat added to the PCM during charging for each TES tank.

Paraffin	RT30	RT28HC	Wax	RT58	P56-58
Heat capacity of PCM (J/g K)	1.8	2.0	2.0	2.1	1.84
Heat added to the PCM during charging (J)	68.04	96.00	705.09	835.17	717.60

Table 12. Heat capacity of TES tanks with each paraffin.

Paraffin	RT30	RT28HC	Wax	RT58	P56-58
Heat capacity TES tank (Wh)	0.181	0.256	1.88	2.23	1.91

Figure A1. Phase distribution of TES tank using paraffin RT30.

Figure A2. Phase distribution of TES tank using paraffin RT28HC.

Figure A3. Phase distribution of TES tank using paraffin WAX..

Figure A4. Phase distribution of TES tank using paraffin RT58.

Figure A5. Phase distribution of TES tank using paraffin P56-58.

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