The general set up for a CFD simulation consists of a model generator, a CFD solver and a post‒processor. In this study, ANSYS‒FLUENT was used as the CFD solver. Discretization of the terms of the governing equations into algebraic forms in the ANSYS‒FLUENT handles using a control-volume-based technique to convert the governing equations to algebraic equations that can be solved numerically. The control volume technique consists of integrating the governing equations for each of cell (control volume), discrete equation that conserve each quantity on a control‒volume basis (ANSYS FLUENT 2015). In the other hand, ANSYS-FLUENT uses a control volume approach (also referred to as a finite volume approach) to calculate the dependent variables (e.g. T, v) at the centre of each cell; however, these variables are needed at cell faces to compute fluxes. A second order upwind discretization scheme is employed to compute variables at the momentum, density and energy. The second order upwind scheme uses a Taylor series expansion of the variable about the cell face to compute flux values. The SIMPLE algorithm was used for the pressure–velocity coupling (ANSYS FLUENT 2015). The SIMPLE algorithm initially solves for a velocity field using a given pressure field, and velocity field. This will give an intermediate velocity field. The final solution for the velocity field must satisfy the continuity equation. Once the pressure correction is found, a velocity correction is
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calculated. Finally, all other equations are solved using the updated pressure and velocity fields.
6.4.1 Phase change modelling strategy
Two typical methods have been introduced to simulate the latent heat energy release/absorption during phase change processes. In this study, the effective heat capacity method was used to simulate PCM effect. In this way, the effective heat capacity of the PCM as a function of temperature, which was obtained from the DSC measurement, was used in the calculations.
In fact, phase changes were modelled through a simplified approach by which the energy release/absorption associated to the phase change process is considered through artefacts applied to the specific heat capacity term.
The computation of the specific heat capacity of the specimen along the tested temperatures C T( )(J/g K) is made according to Eq.(6.13):
( ) ( ) DSC T sample C T (6.13) WhereDSC T( )
sample the heat flow across the specimen at temperature T from the
thermogram (mW/mg), and
is the heating rate (°C/s). This method allows to implement directly of specific heat capacity curve into the software which is useful since the sensible heat and latent heat are not distinguishable in the DSC output curve (particularly in the hybrid PCM case); therefore, the state of the PCM is not necessary to be defined as all the entire curve is given to the model.6.4.2 Simulation parameter estimation
Even though the experimental program did not encompass testing of a prototype containing a single type of PCM embedded, such situation was tackled in the numerical simulation, as to illustrate the performance advantages of the hybrid PCM concept (HPCMM). Therefore, a single PCM mortar, termed as SPCMM was added to the process of numerical simulations. The single PCM mortar selected for such comparison
117 corresponds to a mix that has been performed and tested in the previous chapter, which contains 18.34 % weight of PCM with melting temperature of 24°C. It is worth to mention that, such a melting temperature (around 24°C) is usually used for human thermal comfort purposes (Vaz Sá et al. 2012, Evola et al. 2014, Jaworski 2014, Cunha
et al. 2015). Furthermore, three fictitious single PCM mortars made of 18.34% of RT10
(here termed as SPCMM10), BSF26 (here termed as SPCMM26) and MC28 (here termed as SPCMM28) distinctly were also considered.
As the experimental program did not include the thermal characterization of single PCM mortars, their properties had to be estimated for the numerical simulations.
In order to support such estimates, specific DSC experiments were conducted on the relevant PCMs: RT10, MC24, BSF26 and MC28. One specimen per each type of PCM was considered and the weight of the prepared specimens was of 4.185 mg, 5.76 mg, 5.271 mg and 5.126 mg for RT10, MC24, BSF26 and MC28 respectively. The applied program for DSC testing was analogous to those already made for mortars (detailed in chapter 4). The graph of Figure 6-4a shows that obtained results are in accordance with the characteristics given by the manufacturers (Microthermic 2012, Rubitherm GmbH 2012).
In order to estimate the specific heat capacity curve of single PCM mortars (to be used in the numerical simulations), the method forwarded by (Tittelein et al. 2015) was utilized. It consists in a proportional mixing law for the specific heat, based on the constituents of the mortar, their weight proportions and their individual specific heat capacities. Therefore, the specific heat capacity of the mortar can be estimated through Eq.(6.14):
specimen PCM PCM mortar mortar
C C W C W (6.14) Where Cspecimenis the specific heat capacity of the specimen (J/kg K); CPCMis the specific heat capacity of the PCM (J/kg K); WPCMweight ratio of the PCM to the specimen; Wmortar mass fraction of the plain mortar and Cmortaris the specific heat capacity of the plain mortar (J/kg K). Therefore, the specific heat capacities that were considered for the mortars are presented in the Figure 6-4b.
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For the particular case of SPCMM, values of relevant properties were obtained from a chapter4 with this mortar: density of 1360.9 kg/m3 and thermal conductivity of 0.3 W/m K. And also these values were considered with same quantities for other single PCM mortars with RT10, BSF26 and MC28.
(a) (b)
Figure 6-4: (a) Specific heat capacities calculated with the DSC outputs for the pure PCM specimens (RT10, MC24, BSF26 and MC28); (b) Estimated specific heat capacity curves of the
single PCM mortars.