Physically-based modelling of the system

On the basis of the time-separated working, two distinct models have been elaborated for swimming pool — and kindergarten operations (Figs 2-3), which are shown next in details. The problem was carried out by the MATLAB® and, for some particular calculations, by the MAPLE® software packages.

In Figs 2-3 the following notations were applied:

Ig — global irradiance on collectors’ plane, W/m2;

Ta — outside, ambient temperature, °C;

W — wind velocity, m/s;

Ф — relative humidity of air;

m c — mass flow in collector loop, kg/s;

Vp — volumetric flow in swimming pool loop, m3/s;

Tm — temperature of control room, ambience of the heat exchangers, °C; Th, p,m — swimming pool heat exchanger, pool side, inlet temperature, °C;

V& — domestic hot water load, m3/s;

To — temperature of control room, ambience of solar storage, °C;

Tt — water supply inlet temperature, °C;

Tsout — outlet temperature from the storage to the gas heater, °C.

Both models can be run with inputs either determined by meteorological models or available from measurements. According to the notations above, in the case of calculations by meteorological models, one should give only the number of day (1-365) from that the model can determine the inputs required by the model of the system. These calculations, noted by the block “Meteorological models” are carried out by relations in relevant literatures [1], [2]. As a result the outputs noted at the end of the block are realized. The database underlying for the taken over meteorological models as well as the term clear day occuring later in this paper can be found in [3].

The block “Measured data” represents the case when the inputs for the system are from measurements. The input of the block is a particular date that monitored data, which constituting outputs for the block, are available for. It should be noted that the measurements of the system pertains to the ordinary control method used generally in practice, which operates with fixed switching on and off temperature differences between the collector fluid and the actual consumer.

The outputs of the so far discussed blocks constitute the inputs of the blocks “Model of the system for swimming pool operation” and “Model of the system for kindergarten operation”, from which we get the calculated temperatures of the swimming pool water and the solar storage as outputs. In case the inputs of the blocks are measured data, it makes sense to compare the calculated swimming pool temperature with the measured input temperature at the swimming pool side of the pool heat exchanger noted by T11 in Fig. 1. The temperature of the swimming pool is directly not monitored.

The model assumes well mixed, with homogeneous temperature, swimming pool.

Likewise it makes sense to compare the calculated solar storage temperature with the measured output temperature from the storage noted by T10 as there is no temperature measurement inside. The model assumes well mixed, with homogeneous temperature, solar storage.

Temperatures T11 and T10 also make part as system inputs on Fig. 2 and Fig. 3, but certainly are not considered in calculations. They only play comparison purposes with the relevant calculated results. Dashed lines are used on figures to note that, as outputs of the model of the system, arbitrary variables, either monitored or determined by calculations at any part of the model, can be queried.

According to the inner structure of the models, the working of the different parts can be looked through in the following manner, mentioning the references playing as sources for the sub-models. The main system units have been located in distinct sub-models, that can be used independently too. Such parts are the collector sub-model [4], the heat exchanger sub-model [5] both in swimming pool and in kindergarten operations, the swimming pool sub-model [6], [7] and the solar storage sub-model [5]. There is also a particular sub-model for determining the cooling and delaying effects of the “long” pipelines in the system applying the adequate one dimensional partial differential equation [8] relating to energy conservation law. There is actually a 75 meters distance along pipeline between the kindergarten heat exchanger and the solar storage tank.

Several relations discussed in reference [2] have played as a source for several details.

The model elaborated by the aforementioned description determines and takes into account all energy components influencing the performance and efficiency of the solar heating system. At the swimming pool side these are the evaporation-, radiation-, convection-, conduction-, recovery water heat losses, the active, gained by the solar installation, and passive solar gains. The irradiated energy on collectors’ plane, utilized energy by the collectors, transferred energy in the heat exchanger and relevant losses as well as solar energy directly used up by the consumers are also determined. The possibility of auxiliary heating according to the all-time consumptions is also involved in the model. Because of limits in volume the specification of the describing equations, which can be found in the referenced literatures, is omitted now.

2. Results and discussions

In this paragraph the validation of the model is discussed along with the special effect of the evaporation heat loss coefficient at the swimming pool.