carried out. It was necessary to carry out the 1D simulation of the electrical properties as these could not be determined by the 3D modelling. The study of the effects of environmental variations such as the temperature and irradiation on electrical parameters was undertaken one at a time, while others are kept constant. This is only possible with 1D modelling and simulation. The simulated results were then validated against the manufacturersβ data sheet. Since these were positively verified within limits of acceptable tolerance, these validated parameters were then used as part of the simulation input for the 3D simulation on COMSOL Multiphysics, version 5.1. The details on this are given in chapter 6 of this thesis.
3.3 Three-dimensional modelling of a concentrated thermal photovoltaics energy system
The 2D existing model for the CTPV with COMSOL was re-modelled and the results were validated against COMSOLβs results. The results were validated and in agreement with the existing results. In the re-modelling and simulation of the CTPV system, the 2D model of the CTPV was modelled for every segment of the CTPV system such as the heater, the mirrors, the PV cells and insulation. The CTPV geometry was modelled with its other different components. Selections were developed for the domains and boundaries which were used in implementing materials settings and boundaries conditions, using the COMSOL software.
The selected physics was heat transfer with surface-to-surface radiation interface. Thereafter, the CTPV model in 3D was developed from the 2D CTPV model, using the same approach. This ensured that the modelling parameters for 2D and the 3D of the CTPV could be compared directly one to the other.
3.3.1 Basic Modelling consideration for CTPV model, using COMSOL Multiphysics software
The basic simulation workflow for the 2D model of the CTPV, using COMSOL Multiphysics software, follow the same pattern as already shown in the chart in Figure 2-9. The heat radiated on the PV
35 cells is not fully converted into electric power but it is wasted away as radiation, conduction and/or convection and most often raises the temperature of the PV material and the material becomes hot. This heat reduces the efficiency of the solar material.
To lessen the temperature effect, the PV cells were cooled with water on their rear surfaces by free convective heat transfer (at the interface with the insulation). All the different boundaries experienced heat by conduction. The model simulated the emitter with a definite temperature, Theater, on the inner boundary. At the outer emitter boundary, radiation (surface-to-surface) was taken into account in the boundary condition. The mirrors were simulated by taking radiation into account on all boundaries and applying a low emissivity. Both the inner boundaries of the PV cells and that of the insulation, used radiation boundary conditions. Nonetheless, the PV cells had a high emissivity while the insulation had a low emissivity. Furthermore, the PV cells converted a fraction of the irradiation to electricity and the remaining part remained as heat loss.
3.3.2 Governing equations for the CTPV model
Heat sinks installed on their inner boundaries simulated this condition by accounting for a boundary heat source, the heat transferred per unit time, q, is defined by in Equation (3.1) [64]:
π = βπΊπππ£ (3.1)
For water-cooling of the PV cells by natural or free convective heat transfer took effect and was as represented in Equation (3.2). According to Newton's law of cooling, the equation for convection (heat transfer per unit surface through convection) is expressed as:
π = βππ΄ππ (3.2)
where π, π΄, βπ and ππ are as defined in the list of Engineering and Mathematical symbols.
The convective heat transfer coefficient (βπ) is dependent on the type of medium, liquid or gas, the flow properties such as velocity and viscosity, and any other flow and temperature-dependent properties.
The typical free convective heat transfer coefficient for water and liquids ranges from 50 - 3000 (W/(m2K)) as referenced in the Appendix. In this work, h value of 50 was used.
The PV cellβs voltaic efficiency is a function of the local temperature, having a maximum of 0.2 at 800 K and it is mathematically expressed as:
πππ£= { 0.2 [1 β (800 πΎπ β 1)2] π β€ 1600 πΎ
0 π > 1600 πΎ (3.3) where,
800 K is the PV cell maximum temperature.
At the outer boundary of the PV cells, water cooling by convection was applied to the model which satisfied the convective heat transfer with the water cooling equation defined as:
π0= β . ( πππ₯π‘β π) (3.4)
where,
36 The heat flux is π0 and the heat flux is for any fluid which can be liquid or gas/air.
β = βπ€ππ‘ππ (π·, πππ₯π‘ ) (3.5)
For water, h takes value, βπ€ππ‘ππ between 500 and 10,000 W/m2K πππ₯π‘ = external or ambient temperature = 293.15 K
Lastly, at the outer boundary of the insulation, convective cooling for air with h set to 5 W/(m2Β·K) and Tamb to 293 K, were applied.
3.3.3 Properties of CTPV materials
The materials definitions used in the model are listed below. Their references and relevant material properties are attached in the Appendices.
Table 3-1: Material properties summary [64]
Component k [W/(mΒ·K)] Ο [kg/m3] Cp [J/(kgΒ·K)] Ξ΅
Emitter 10 2000 900 0.99
Mirror 10 5000 840 0.01
PV Cell 93 2000 840 0.99
Insulation 0.05 10 100 0.1
The parametric solver was used by the model to calculate the stationary solution for a list of emitter temperatures (1000 K to 2000 K). The graph in Figure 2-10 shows the temperature distribution that changed with the operating condition within the CTPV system. The upper (right side) of the graph in Figure 2-11(b) investigates what the optimal operating temperature would be and illustrates the stationary distribution at working conditions with an emitter temperature of 2000 K. Further various parameters changes could be effected and investigated; such as the number of mirrors used, the number of PV cells used, the type of coolants used and so many other changes could be investigated to predict the CTPV performances with those changes. The results were post-processed and various graphs plotted, analysed and discussed.
3.3.4 The three-dimensional CTPV model
The 3D CTPV model was developed by determining and selecting the physics, using the same material properties for the 2D configuration. The materials physics could be chosen from COMSOL library or could be user-defined. This was followed by meshing and simulation, the details of which are given in Chapter four. As the materials selection and definitions are the same for the 2D and 3D models, the same physics on selected materials apply for the 2D and 3D models.
The same procedure of modelling and simulation as illustrated in the basic modelling workflow in Figure 2-9 was similarly followed for the 3D after importing the modelled 2D geometry into the COMSOL environment. The obtained results were post-processed, analysed and discussed. However, the number of points generated for the domain, boundaries, edges and points in the 3D modelling were greater than in the 2D model.
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