In the proposed solar-assisted domestic hot water system (Figure 1), thermal energy is primarily harvested by a flat-plate solar collector and transferred to a stratified storage tank through an internal heat exchanger located in the lower part of the tank, with circulation ensured by a dedicated pump in a closed solar-fluid loop.

Figure 1.

Layout of the solar collector system: main components and fluid loops

In order to ensure domestic hot water availability under low solar energy availability, a natural gas boiler supplies auxiliary heat to a second internal heat exchanger positioned in the upper part of the tank, again via a dedicated pumped closed loop. Cold water from the mains is routed through a diverter that splits the flow between direct charging of the tank at its bottom and a branch feeding a mixer; simultaneously, hot water drawn from the top of the tank is directed to the mixer, where it is blended with mains water to deliver domestic hot water to the user at the required temperature. The proposed system layout is suitable and universal for all climates because the fluids used for heating the water are decoupled, and in this way mains water flows only inside the tank and diverter-mixer setup.

In particular, the layout under evaluation comprises multiple hydraulic circuits, identified as follows:

• SCF, Solar Collector Fluid (a mixture of 40% propylenic glycol in water), is the heat transfer fluid circulating in the solar thermal loop (between SC, P1, and the lower internal heat exchanger of TK);

• NGBF, Natural Gas Boiler Fluid (pure water), is the heat transfer fluid circulating in the auxiliary boiler loop (between NGB, P2, and the upper internal heat exchanger of TK);

• MW, Mains Water, is the cold potable water supplied from the aqueduct and routed to the system through the diverter (D);

• HW, Hot Water, is the hot water withdrawn from the upper part of the storage tank and sent to the mixer (M);

• DHW, Domestic Hot Water, is the tempered sanitary water delivered to the end user downstream of the mixer (M).

• Furthermore, the system incorporates the following primary components:

• SC, Solar Collector, a flat-plate solar thermal collector providing renewable heat to the storage system;

• TK, Tank, a storage tank containing water and equipped with two internal heat exchangers:

• A bottom coil coupled to the solar collector loop (SCF);

• A top coil coupled to the natural gas boiler loop (NGBF).

The control strategy of the investigated system is based on the following assumptions, pointing out the way how the system operates:

• P1 is activated when the temperature difference between the outlet of the solar collector and the temperature inside the tank at the inlet to the internal heat exchanger of TK overcomes a fixed upper dead band, and it deactivates then the same difference decreases to fixed lower dead band;

• P2 and NGB are activated once the temperature difference between the fixed set point temperature of TK and the top part of TK increases to a certain upper dead band, and they are deactivated when the same difference decreases to a certain lower dead band;

• NGB provides NGBF at a fixed temperature suitable to heat the water in TK top part to the fixed set point temperature;

• D and M are operated in order to keep the temperature of DHW exiting the system at a constant value (as a thermostatic valve), diverting and mixing the mains water, respectively.

To perform the dynamic simulation of the solar-assisted domestic hot water (DHW) setup, the system was modelled in the widely adopted TRNSYS environment, which is extensively used for the analysis of conventional and advanced thermal systems. The modelling workflow follows the same general approach typically adopted in TRNSYS studies: starting from the conceptual layout of the plant, the required input data were defined (i.e., weather data, technical parameters of the components, and user demand profiles), then the numerical model was implemented by interconnecting available TRNSYS library components, and finally the simulation outputs were post-processed as both dynamic trends and integrated performance indicators. For sake of brevity, in this section only the overall energy and economic model of the system has been presented in detail.

The developed model reproduces the operation of a solar collector loop charging a storage tank through a lower internal heat exchanger, while an auxiliary natural gas boiler loop provides additional heat through a second internal heat exchanger located in the upper part of the same tank. The sanitary cold water from the mains is routed through a diverter that splits the flow into (i) direct tank charging at the bottom and (ii) a branch feeding a thermostatic mixer, which also receives hot water drawn from the top of the tank, delivering DHW at the required supply temperature.

The TRNSYS implementation relied entirely on validated built-in component models. In particular, the flat-plate solar collector was modelled using Type 539, which calculates collector thermal output as a function of incident solar radiation, ambient conditions, inlet temperature, and collector parameters, including thermal capacity. The storage tank was represented by Type 60d, enabling a stratified thermal storage simulation (10 nodes for tank vertical discretization) with internal heat exchangers positioned at the bottom (solar loop) and top (boiler loop), thus capturing the key dynamic effects of stratification on DHW production. The auxiliary natural gas boiler was modelled using Type 122, providing thermal power to the boiler loop based on a control signal and accounting for efficiency characteristics. Pumps for both the solar loop and boiler loop were implemented with Type 114, which allows the definition of mass flow rate and electrical consumption (when required) under an external control signal. The diverter and the mixer were implemented with Type 11f and Type 11h, respectively, to represent the flow splitting of mains water and the mixing process to achieve a target DHW delivery temperature. The DHW load was imposed through Type 9e, which provides a prescribed draw-off profile over time. Weather boundary conditions (ambient temperature, solar irradiance on the collector plane and mains temperature) were provided via Type 15-3 processing .epw files.

The control logic was implemented using Type 165 on/off controllers, which were used to manage pump and boiler operation according to the selected temperature-based control strategy, enabling the solar loop when collector outlet temperature exceeds the tank bottom temperature by a fixed differential, and enabling boiler charging when the tank top temperature falls below a DHW setpoint. The DHW outlet temperature downstream of the mixer was monitored using an additional Type 114 instance used as a temperature-reading/handling block for the delivered water stream.

To support performance assessment, key energy flows (e.g., heat transferred by the solar loop, heat provided by the boiler, and useful heat delivered as DHW) were integrated over the simulation horizon using Type 24, allowing the derivation of cumulative energy indicators from instantaneous thermal power variables. Results were visualized through Type 65d (online plotting of relevant state variables such as tank node temperatures, loop temperatures, mass flows, and control signals) and exported with Type 25c for post-processing and reporting.

The adopted component models are part of the TRNSYS standard libraries and are based on manufacturer data and/or prior validation processes, thus they provide a robust basis for predicting the transient behaviour and overall performance of the investigated solar-assisted DHW system.

The analysis of the system performance has been carried out assuming realistic domestic hot water demand for household users. Demand profiles for the user type studied in this paper were taken from existing literature [18]. In particular, three representative average user profiles, recorded at 5-minute intervals, were used to construct the domestic hot water (DHW) demand. The profiles were then normalized to define the demand, assuming water use equivalent to four occupants with a specific consumption of 50 kg/day per person at 45 °C. The resulting DHW demand is shown in Figure 2.

Figure 2.

Domestic hot water dynamic profile

The simulation of the weather conditions for capitals of 34 countries was performed on the basis of weather files in .epw format taken from PVGIS portal [34] and implemented in TRNSYS. The selected locations have been listed in Table 1, where main climatic data has been included, as mean ambient temperature, mean mains temperature and horizontal yearly irradiance.

For the technical parameters of solar thermal collectors and tank manufacturer data were used. In particular, for the flat-plate solar collectors parameters of commercially available unit have been used (VITOSOL 200-FM Model SV2F [35]), and the same approach has been used for the tank with two internal heat exchangers (Vitocell 100-B/100-W 300 l [36]).

As concerns the system design, the parameters of the collector setup, tank and control system have been set to allow a proper operation of the system and to cover a part of the domestic hot water demand. The main system parameters have been listed in Table 2.

In order to perform the simulations under the same conditions for both cases of mains water temperature (dynamic and constant), the same initial temperature regime has been assumed for SC and TK. From the top to the bottom nodes of the tank the following temperatures have been assumed to 55, 53, 50, 47, 42, 37, 32, 27, 22 and 20 °C, while the initial collector temperature has been set to 20 °C.

The analysis of the effect of mains water temperature has been analysed from the dynamic point of view for the selected day of 17^th February and 19^th August, when the mains dynamic water temperature achieved the maximum variations with respect to the yearly mean ambient temperature.

In Figure 3 and Figure 4 the main temperature trends in the solar collector system for the selected day of 17^th February have been shown for the dynamic and mains constant water temperature assumptions, respectively. The dynamic results allow one to state that the overall effect of mains water temperature is not negligible, though it does not change significantly the temperature trends in the system from the qualitative point of view. The main characteristics of the dynamic operation of the system are primarily affected by the solar radiation intensity, ambient air temperature and DWH demand trends.

For the investigated day of 17^th February, the analysis of results shows that the effect of the mains dynamic water temperature is observable mainly for the temperatures of the system related to the bottom of the tank. In fact, the top tank temperature is practically the same for both cases of mains water temperature, indeed the difference between the average top temperature of the tank is only +0.15 °C between the case of dynamic and mains constant water temperature. This result is achieved despite the significant difference between the constant and dynamic (average) mains water temperature of +3.7 °C. The lower inlet water temperature to the solar collector system induced a lower temperature at the outlet of SC. The difference between the average, maximum and minimum SC outlet temperatures between the case with constant and mains dynamic water temperature are −0.21, −0.73 and 0.00 °C, respectively. Therefore, the mains water temperature does not influence the minimum temperature of the collector achieved at the end of the day. The lower mains water temperature, the lower the bottom TK temperature. In this case, the variation between the average values among the constant and mains dynamic water temperature is 1.8 °C.

Figure 3.

Main temperatures in the solar collector system, 17th February, mains dynamic water temperature over the year

Figure 4.

Main temperatures in the solar collector system, 17th February, mains constant water temperature over the year

A similar analysis has been carried out for the representative day of 19^th August (Figure 5 and Figure 6). During the investigated day, the average value of the mains dynamic water temperature is 5.7 °C higher than the constant one assumed equal to the mean ambient temperature, which is significantly higher than the variation observed in the winter day. For this reason the effect on the collector system temperature regime is higher. Indeed, for the bottom TK temperature, the difference between the average, maximum and minimum values of dynamic and mains constant water temperature is 3.4, 1.8 and 6.7 °C, respectively. This influences the output temperature of SC, with is averagely higher by 0.43 °C in case of mains dynamic water temperature compared to the constant one. Moreover, the comparison of the trends of TK top temperature points out a difference of 0.68 °C between the average values of dynamic and constant cases.

Figure 5.

Main temperatures in the solar collector system, 19th August, mains dynamic water temperature over the year

Figure 6.

Main temperatures in the solar collector system, 19th August, mains constant water temperature over the year

The monthly results presented in Figure 7 and Figure 8 confirm that the boundary condition adopted for the inlet water temperature has a measurable impact on the performance of the solar collector installation for the production of domestic hot water. In the constant-temperature case, the inlet temperature is fixed at 9.7 °C, whereas the dynamic profile exhibits an evident seasonal evolution, ranging from 6.1 – 6.8 °C in January – March to 14.5 – 15.4 °C in July – August. Consequently, the constant assumption overestimates the inlet temperature in the winter season and underestimates it in the summer season, and this affects both the estimated temperature increase needed for DHW preparation and the effective thermal load matched in part by the solar loop.

In winter, when the monthly averaged mains water temperature remains about 3 °C below the constant value, the simulated monthly thermal energy produced by SC is slightly higher under dynamic conditions: the energy produced under dynamic mains temperature exceeds the one achieved under constant conditions by about 3.5 and 4.9% in January and February, respectively. The same tendency is reflected by the solar collector thermal efficiency, being higher in dynamic scenario by comparable relative amounts. As the season progresses, the difference in energy production reduces and changes sign. In April, in the dynamic case, the energy production of SC becomes marginally lower than the one in the constant case, and from May onwards the useful solar heat delivered to the tank is systematically reduced with respect to the constant-temperature assumption. The largest deviations occur in the central summer months, when the dynamic inlet temperature is about 5 °C higher than the constant value and the SC thermal output is 9 – 10% lower. Over the entire year, this effect dominates, leading to an annual solar production of 1309.8 kWh for the dynamic case compared to 1396.4 kWh for the constant case, with a reduction of −6.2%, and to a slightly lower mean collector efficiency, 0.401 versus 0.420.

Conversely, the solar factor is higher in every month when the dynamic mains temperature is adopted. The increase ranges from about 12% in May to about 23% in January, and remains substantial in summer, where the maximum solar factor is observed in July, being 0.851 and 0.736 in dynamic and constant mains water temperature scenario, respectively. This behaviour indicates that, although a warmer dynamic inlet condition reduces the recoverable solar heat in warm months, it reduces the overall DHW heating requirement and the auxiliary contribution even more, thus increasing the solar share. Overall, the mean monthly solar factor rises from 0.358 to 0.416, thus by +16.1%, when dynamic mains temperature is considered, highlighting that the constant-inlet assumption may overestimate summer solar yield while simultaneously underestimating the solar contribution.

Figure 7.

Thermal energy produced monthly by SC in case of dynamic and constant temperature of mains water, mean monthly mains temperature and constant yearly ambient temperature

Figure 8.

Thermal efficiency and solar factor of solar collector in case of dynamic and constant temperature of mains water

The yearly results obtained for the 34 European capitals indicate that the representation of mains water temperature constitutes a relevant modelling assumption, since the mean dynamic value of the mains water temperature is systematically higher than the constant one adopted a simplified approach for modelling mains water temperature.

The difference among dynamic and constant assumption ranges from about 0.6 °C in northern locations (like Stockholm) to more than 4 °C in Mediterranean climates (as Athens). As expected, the higher inlet temperature in the dynamic case reduces the temperature lift required for DHW preparation and leads to a consistent decrease of the yearly thermal demand, with the dynamic case always lower than the constant one by approximately 560 – 750 kWh, which is about 20% on average basis. This condition propagates directly to the contribution of NGB as an auxiliary heat, in fact the contribution in the dynamic scenario is lower than the constant one for all locations, typically by 22 – 38%. The effect is particularly noticeable in colder climates where the auxiliary heater dominates the energy balance, For example, in Vaduz and Vilnius the boiler production decreases from about 2650 and 2620 kWh (constant case) to 2010 and 2040 kWh (dynamic case), respectively. In warmer climates the auxiliary energy is smaller, however the difference remains significant, as shown by Athens, from 680 to 450 kWh, and Madrid, from 873 to 584 kWh, when constant and dynamic cases are compared.

A coherent trend is also observed for the solar contribution. In all locations, the thermal energy produced by SC in case of mains dynamic water temperature is lower than the constant one, with an average reduction of about 8%. The magnitude of the decrease increases with the difference between dynamic and constant temperature cases, reaching the largest values in southern capitals, as Madrid and Athens), whereas northern locations exhibit more limited deviations, like Stockholm. In contrast, tank thermal losses tend to increase when dynamic mains temperature is considered, with the dynamic case exceeding the constant one by roughly 20% on average and maximum increments again occurring in warm climates. This behaviour is consistent with a reduced draw-off driven cooling effect and longer periods at elevated storage temperatures. Overall, the constant inlet-temperature assumption leads to a systematic overestimation of annual DHW demand and, consequently, of both solar and boiler heat supplied, while underestimating storage losses, with deviations that become more pronounced as the climatic difference between dynamic and constant cases increases.

The yearly energy and economic indicators and their variation between dynamic and constant case presented in Table 5 and Table 6, respectively, confirm that the inlet-water temperature assumption affects not only the energy flows but also the energy and economic performance of the solar-assisted DHW system. For all locations, the mean dynamic mains temperature is higher than the constant value adopted in the simplified approach, reducing the annual temperature increase required for DHW preparation. As a consequence, both the reference system and proposed system operating costs decrease when the dynamic mains temperature is considered. On average, the operation cost of the reference system under dynamic case is 288 EUR/year compared to 357 EUR/year in the constant temperature case, while for the proposed system decreases from 203 to 152 EUR/year. The reduction is larger for the reference system, with a mean of about 69 EUR/year, than for the proposed system, where the mean is about 51 EUR/year, so the annual saving attributed to solar integration is lower under the dynamic assumption. The mean operation cost saving is 136 EUR/year in the dynamic case and 154 EUR/year in the constant case, i.e., the constant-temperature approximation overestimates the expected saving by about 13% on average. This difference increases with the gap between dynamic and constant mains water temperature and is most relevant in warm capitals, where the constant inlet temperature is distinctly lower than the realistic mains profile. In Lisbon and Rome the saving decreases from 263 and 254 EUR/year (constant) to 221 and 212 EUR/year (dynamic), respectively. Madrid and Athens show reductions of about 32 and 34 EUR/year, whereas in locations with smaller temperature offsets the difference is limited to a few euros per year. From a performance point of view, the dynamic inlet condition yields a lower yearly collector efficiency due to reduced useful heat extraction in warm periods, while the solar factor increases, reflecting the stronger reduction of auxiliary contribution relative to total DHW requirement. In general, adopting a constant mains temperature equal to mean ambient temperature tends to overestimate the economic benefit of the solar DHW system, especially in mild and Mediterranean climates. For PS, the mean difference in operation cost between the time-varying and constant mains water temperature cases among the considered locations was +36.6%.