A set of solutions of a reference case which will be called as “one day outdoor test” have been obtained in order to investigate the sensitivity of the numerical solutions on the temporal and spatial discretization adopted.

In the “one day outdoor test” the the ICS is exposed to outdoor sunny weather conditions during 24 hours without draw off. The simulation starts at 6 am (solar time) with the ICSs at an initial and homogeneous temperature jH; indicated by the user. Main features of the test are:

Transient effects are considered.

A constant ambient temperature of Ta = 20°С is assumed during all the day.

A daily solar irradiance in the collector plane of Я( = 25000kJ/m2 is assumed. Sunrise and sunset are set at 6 am and 6 pm. is assumed normal beam radiation, and is distributed during the day according to standard radiation correlations [2].

Among others values that can be obtained from the test, the following will be commented:

• Temperatures: T„: ambient temperature; Тет: average temperature of the water in the store; To()S: average temperature in the absorbing surface; : average temperature in the back surface; Tt: average temperatures in the top surface; and T6: average temperature in the bottom surface.

• Terms of the energy balance

(9)

where Eas is the accumulated energy by sensible heat at the water store, and Qt and Qi are respectively the thermal losses through the front surface (cover) of the store and through the other surfaces of the store respectively.

With the daily integrated values of the terms of the energy balance, the daily efficiency can be calculated as the ratio between the accumulated energy at the end of the day and the daily solar irradiance Я(.

In the results reported in this subsection the following data has been adopted: Я(= 25.000 ;Ta= = C; =1.8 and [/«=0.6387 W/mK. The store has a length (L)

of 1000 mm and a width ( ) of 100 mm.

A set of solutions of the “one day outdoor test” has been obtained varying the temporal and spatial discretization following an h-refinement procedure, that is, all other numerical parameters (numerical scheme, convergence criteria..) are fixed, and the mesh (spatial or temporal) are intensified. The study of temporal and spatial discretization was decoupled. Firstly the time step was fixed and the mesh was progressively refined. Once the spatial discretization was selected, the influence of the temporal discretization was analysed. The mesh was fixed and the time-step refined.

In the first step, three levels of refinement were considered (n = 5,10,20). Calculated values of the terms of the energy balance 9 are presented in Table 1. They are given integrated over the day and normalised with the daily solar irradiance Я(. As it can be seen, while for all levels of refinement the integrated terms of the energy equation obtained are almost the same, some differences appear in the maximum temperatures achieved during

the simulation. These differences are less important for the second and third levels of mesh refinement, n=10 and 20.

The computational time (CPU time) to perform the numerical simulations for the three levels of refinement was respectively: 39, 152 and 851 minutes in a AMD K7 2600 MHz processor.

Due to the level of accuracy obtained and the computational costs commented above, the second level of refinement was selected to analyse the influence of the temporal discretiza­tion. Three time-steps were taken into account (At= 1, 2, and 4 seconds). Results of this verification analysis is presented in table 2. As observed, while almost no differences ex­ist between results considering time-steps of 1 or 2 seconds, important disagreements are obtained when a time-step of 4 seconds is used.