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Research Papers

# Numerical Investigation and Nondimensional Analysis of the Dynamic Performance of a Thermal Energy Storage System Containing Phase Change Materials and Liquid Water

[+] Author and Article Information
Hebat-Allah M. Teamah

Department of Mechanical Engineering,
McMaster University,
e-mail: teamahhm@mcmaster.ca

Marilyn F. Lightstone

Department of Mechanical Engineering,
McMaster University,
e-mail: lightsm@mcmaster.ca

James S. Cotton

Department of Mechanical Engineering,
McMaster University,
e-mail: cottonjs@mcmaster.ca

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received April 21, 2016; final manuscript received August 18, 2016; published online November 10, 2016. Assoc. Editor: Jorge E. Gonzalez.

J. Sol. Energy Eng 139(2), 021004 (Nov 10, 2016) (14 pages) Paper No: SOL-16-1179; doi: 10.1115/1.4034642 History: Received April 21, 2016; Revised August 18, 2016

## Abstract

The dynamic performance of a thermal energy storage tank containing phase change material (PCM) cylinders is investigated computationally. Water flowing along the length of the cylinders is used as the heat transfer fluid. A numerical model based on the enthalpy-porosity method is developed and validated against experimental data from the literature. The performance of this hybrid PCM/water system was assessed based on the gain in energy storage capacity compared to a sensible only system. Gains can reach as high as 179% by using 50% packing ratio and 10 °C operating temperature range in water tanks. Gains are highly affected by the choice of PCM module diameter; they are almost halved as diameter increases four times. They are also affected by the mass flow rate nonlinearly. A nondimensional analysis of the energy storage capacity gains as a function of the key nondimensional parameters (Stefan, Fourier, and Reynolds numbers) as well as PCM melting temperature was performed. The simulations covered ranges of 0.1 <  $Stẽ$  < 0.4, 0 < Fo < 600, 20 < Re < 4000, $0.2<(ρCP)*<0.8$, and $0.2<θm<0.8$.

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## Figures

Fig. 1

The studied domain in the code (a) the whole tank and (b) zoomed view of the cylindrical jacket

Fig. 2

Isothermals in PCM modules (Vtank=0.2 m3, packing ratio=30%,Tst=40 °C, Tin=52 °C ,Tm=42 °C, ṁ=0.05 kg/s) [melting point is shown in dotted line]

Fig. 3

Local analysis of melting behavior in PCM modules (Vtank=0.2 m3, packing ratio=30%,Tst=40 °C, Tin=52 °C ,Tm=42 °C, m˙=0.05 kg/s): (a) Local molten fraction, (b) local heat transfer rate, and (c) radial temperature distribution in 4/5 of height of PCM module

Fig. 4

Overall melting performance behavior (Vtank=0.2 m3, packing ratio=30%,Tst=40 °C, Tin=52 °C ,Tm=42 °C, m˙=0.05 kg/s): (a) Overall molten fraction, (b) slope of molten fraction with time, (c) overall heat transfer rate to PCM, and (d) tank outlet temperature

Fig. 5

Energy storage gain of hybrid system relative to the only water system (Vtank=0.2 m3, packing ratio=30%,Tst=40 °C, Tin=52 °C, ΔTop=12 °C , m˙=0.05 kg/s): (a) Evolution of energy with time in the system components and (b) Instantaneous gain with time

Fig. 6

Analytical gains for different PCM volume fractions and temperature ranges using lauric acid (Table 2)

Fig. 7

Melt fraction and gains in a 200 l tank having 50% PCM (Tst=20 °C, Tm=(Tst+Tin/2), ΔTop=Tin−Tst, m˙=0.05 kg/s  ): (a) Molten fraction and (b)Gains

Fig. 8

Melt fraction and gains for different mass flowrates in a 200 l tank having 50% PCM(Tst=20 °C, Tm=(Tst+Tin/2), ΔTop=Tin−Tst): (a) m˙ = 0.05 kg/s (base case) and (b) m˙ = 0.1 kg/s

Fig. 9

Melt fraction and gains for different module diameters in a 200 l tank having 50% PCM (Tst=20 °C, Tm=(Tst+Tin/2), ΔTop=Tin−Tst, m˙=0.05 kg/s): (a) D = 2 cm (base case), (b) D = 4 cm, and (c) D = 8 cm

Fig. 10

Melt fraction and gains for different melting temperature choice in a 200 l tank having50% PCM (Tst=20 °C, m˙=0.05 kg/s, ΔTop=Tin−Tst,  D=8 cm, m˙=0.05 kg/s): (a) Tm=(Tst+Tin/2) and (b) Tm=(3Tst+Tin/4)

Fig. 11

Gains for different heat transfer fluids in a 200 l tank having 50% PCM (Tst=20 °C, m˙=0.05  kg/s, ΔTop=Tin−Tst,  D=2 cm, , m˙=0.05 kg/s ): (a) ρHTFCP, HTF=4.2 MJ/kg (base case), (b) ρHTFCP, HTF=3.1 MJ/kg, (c) ρHTFCP, HTF=2.1 MJ/kg

Fig. 12

Nondimensional map for the expected gains of the system as a combination of key parameters

Fig. 13

Schematic of the experimental facility studied by Jones et al. [39]

Fig. 14

Comparison of predictions from present code against experimental data of Jones et al. [39]: (a) average molten fraction, (b) melt front at 3120 s, (c) melt front at 7200 s, and (d) melt front at 10,800 s

Fig. 15

Comparison of predictions of stored energy from present code and Esen et al. [42]

Fig. 16

Grid independence test on average molten fraction (Vtank=0.2 m3, packing ratio=30%,Tst=40 °C, Tin=52 °C , m˙=0.05 kg/s)

Fig. 17

Effect of wall material on hybrid system total energy (Vtank=0.2 m3, φ=30%,Tst=40 °C, Tin=52 °C , m˙=0.05  kg/s,Rc, inn = 1 cm, Rc, out=1.1 cm)

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