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M.M. Kenisarin, et al. Journal of Energy Storage 27 (2020) 101082 Table 12 Parameters of HTF and PCM during melting tests [124]. HTF mass flow rate (kg/s) 0.058 0.052 0.056 0.054 PCM initial temperature ( ̊C) ̶28 ̶27 ̶27 ̶28 HTF inlet temperature ( ̊C) 18 12 11 8 Effective thermal conductivity (W/mK) 1.9 1.3 1.21 1.1 the effective thermal conductivity in modeling the melting heat transfer of water inside spherical capsule permits to simplify the mathematical modelling the packed bad LHSS. These studies stimulated set new re- search on the effective thermal conductivity of PCMs. Amin et al. [124] using CFX Ansys 12-1 program developed a CFD simulation model of heat transfer in phase change material contained in a spherical capsule. In the developed model, the buoyancy forces of the PCM are ignored. The PCM was set as a homogeneous binary mixture of water and ice, with the default thermal properties of 0 ̊C reference temperature. Therefore, the density, thermal conductivity, and other properties of the PCM were assumed constant in the numerical simu- lations, which only varies marginally over the temperature range con- sidered. For validation of simulation results, the experimental study of charging (solidifying) and discharging (melting) modes in the spherical thermal energy storage capsule of 74 mm in diameter and 2.5 mm thickness has been conducted. Glycol solution was used as heat transfer fluid while the water was served as the PCM. The experimental test results are given in Table 12. Comparing melting tests to the SFD modeling results, it was suggested the following empirical correlation for estimation of the effective thermal conductivity of the PCM (water) in the spherical enclosure: keff = 0.3847·10 7·Ra + 1.5859. (55) k The equation is valid for 6.8 × 106 < Ra <4.4 × 107. The hy- draulic diameter of the PCM used for calculation Rayleigh number Dpcm is the inner diameter of the sphere. Liao et al. [125] studied numerically the constrained melting pro- cess of the PCM (NaNO3) in a spherical shell (steel) with an inner diameter 50 mm and a shell thickness of 0.2 mm. The numerical modeling results is then validated by comparing with the experimental data obtained by Fan et al. [119] for n-octadecane as the PCM (Fig. 58). Fig. 58. Comparison of the liquid fraction during the melting process between the Fan et al. [119] result (Exp. [10]) and the simulating result of Liao et al. [125] (Pre.). Fig. 59. Comparisons of melting fractions predicted by correlation (57), NC model and the results for the melting inside a sphere obtained in other works [126]. As seen in Fig. 58, the results predicted by the used simulation model agree well with experimental results, and deviation is smaller the 3%. Based on this comparison, it was proposed for estimating the effective thermal conductivity the following empirical correlation: keff k = 0.174Ra0.323, for103 < Ra < 5 × 108. (56) Here the characteristic length of the Rayleigh number is the gap spacing δ between the solid-liquid interface and the inner surface of the spherical shell. Recently, Gao et al. [126] applied a new approach in developing an effective thermal conduction correlation for the prediction of natural convection affected constrained melting process inside a sphere. In contrast to previous studies [124, 125], the present approach is based on considering the melting fraction α (the dimensionless parameter as it was shown in previous sections) is widely used for the melting problem. The used numerical model was validated by comparison of predicted results with experimental data of Tan [48]. Numerical studies result in the following correlation of the effective thermal conduction was pro- posed 30 keff = 0.129 1.407Ra0.257. k (57) Thecorrelationisvalidfor1.5×104 ≤Ra≤6.3×107;17≤Pr ≤ 550; 0.011 ≤ Ste ≤0.276. Here the characteristic length is δ = =Ro – Ri = =Ro (1– (1– α)1/3). Fig. 59 presents the comparison between the predicted results of Gao et al. [126] for the melting fractions inside a sphere and the results obtained with using correlations of other re- searchers. It is seen that the predictions made by the correlations of Gao et al. [122] and Raithby and Holland [127] are in good agreement with experimental data of Tan [46] and Fan et al. [119]. It is worth notingPDF Image | Journal of Energy Storage 27
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