Anica Trp, Kristian Lenic, Bernard Frankovic
Faculty of Engineering University of Rijeka, Vukovarska 58, HR-51000 Rijeka, Croatia
Phone: + 385 51 651 514, Fax: + 385 51 675 801, E-mail: anica. trp@riteh. hr

Latent thermal energy storage system of the shell-and-tube type with the phase change material (PCM) filling the shell side, which is used as a heat storage device in solar heating applications, has been analysed numerically and experimentally in this paper. The heat transfer in this type of thermal energy storage system is a conjugate problem of transient forced convective heat transfer between the heat transfer fluid (HTF) and the wall, heat conduction through the wall and solid-liquid phase-change of the PCM. Since phase-change heat transfer is non-linear due to the moving phase change boundary, analytical solutions are only known for a few problems with simple geometry and simple boundary conditions. Numerical methods provide a more accurate approach, so various techniques have been developed. Many authors [1] — [5] have used the enthalpy formulation, in which the energy equation for PCM is written in terms of enthalpy. A transient heat transfer phenomenon in a shell-and-tube latent thermal energy storage system has been studied numerically by Bellecci and Conti in [6] — [8], and numerically and experimentally by Lacroix in [9] and [10]. These authors have used an enthalpy method for solving phase-change heat transfer and employed standard empirical correlations to calculate convective heat transfer coefficient. Cao and Faghri in [11] and [12] have simulated numerically, using the temperature transforming model for phase-change heat transfer, the transient behaviour of the shell-and-tube thermal energy storage system employing a low Prandtl number HTF. Ismail and Abugderah in [13] have modelled numerically a phase change thermal energy storage system of the same type. In both papers, the transient HTF momentum and energy equations were solved simultaneously with the tube wall and the PCM energy equations, as one domain, in order to avoid the errors due to the use of empirical correlations. Zhang and Faghri in [14] have semi-analytically studied a shell-and-tube latent thermal energy storage system employing a moderate Prandtl number HTF. They concluded that the laminar forced convective heat transfer inside the tube never reaches a thermally developed state and must be solved simultaneously with the phase-change of the PCM, so the application of CFD methods is required. In [15] a transient phase-change heat transfer with conjugate forced convection in the shell — and-tube latent heat storage unit, with water as HTF and calcium chloride hexahydrate as PCM has been analysed numerically. In this paper, a transient heat transfer phenomenon during charging and discharging of the shell-and-tube latent thermal storage unit has been analysed numerically and experimentally. The mathematical model has been formulated. The enthalpy method for modelling phase-change heat transfer has been used. The dimensionless conservation equations for HTF, wall and PCM, with initial and boundary conditions, have been discretised by fully implicit control volume approach, that has been implemented in developed fOrtRAn computer code, and solved simultaneously using an iterative procedure. Numerical model has been validated with experimental data. Series of numerical calculations have been performed in order to analyse transient phase — change heat transfer during charging and discharging of the latent thermal energy storage unit.

SHAPE * MERGEFORMAT

dWX dWX dWX dP 1 дт x dX R dR dX Re

The governing differential equations of the HTF, the tube wall and the PCM, with initial and boundary conditions, have been solved as one domain. The computational domain has been discretised by the control volume approach and the SIMPLER algorithm. The formulation has been fully implicit in time and the convection-diffusion terms have been treated using power-law scheme. Algorithm has been implemented in developed FORTRAN computer code and the resulting discretisation equations have been solved simultaneously using an iterative procedure. Time-wise temperature distributions of HTF, tube wall and PCM have been obtained by numerical calculations and transient phase — change heat transfer behaviour during charging and discharging of the shell-and-tube thermal energy storage unit, i. e. melting and solidification of the PCM has been simulated.