Experimental Investigation of Thermal Performance for Innovative Spiral Solar Collector

Various parameters and efficiencies will be calculated by fundamental mathematical relations. The heat losses, efficiency, and output temperatures are the main parameters of the present work. Also, the overall heat losses coefficient (U_L) and thermal efficiency $\eta_c$ of the collector can be calculated.

2.1 Collector heat losses

The heat losses from the collector are an essential part for evaluating its efficiency. Three types of heat losses are considered in the calculation procedures. Losses from the upper, lower, and sides surfaces of the collectors are important factors in determining the collector's performance. Hence, the total heat losses from the collector can be expressed as follows [10].

$\mathrm{Q}_{\text {loss }}=\mathrm{U}_{\mathrm{L}} \mathrm{A}_{\mathrm{c}}\left(\mathrm{T}_{\mathrm{c}}-\mathrm{T}_{\mathrm{a}}\right)$     (1)

The overall heat loss coefficient (U_L) can be calculated [11] as follows

$\mathrm{U}_{\mathrm{L}}=\mathrm{U}_{\mathrm{t}}+\mathrm{U}_{\mathrm{b}}+\mathrm{U}_{\mathrm{e}}$    (2)

The energy losses through the upper surface by convection between parallel plates and the radiation across them as in the study of Iordanou [12]. Then, the coefficient of heat losses from the upper surface can be formulated as

$\begin{aligned} & U_t =\left\{\frac{N}{\frac{c}{T_p}\left(\frac{T_p-T_a}{N+f}\right)^e}+\frac{1}{h_a}\right\}^{-1} \\ & +\frac{\sigma\left(\mathrm{T}_{\mathrm{p}}+\mathrm{T}_{\mathrm{a}}\right)\left(\mathrm{T}_{\mathrm{p}}^2-\mathrm{T}_{\mathrm{a}}^2\right)}{\frac{1}{\epsilon_{\mathrm{p}}+0.00591 * \mathrm{~N} * \mathrm{~h}_{\mathrm{a}}}+\frac{2 \mathrm{~N}+\mathrm{f}-1+0.133 \epsilon_{\mathrm{p}}}{\epsilon_{\mathrm{p}}}-\mathrm{N}} \\ & \end{aligned}$    (3)

$c=520 *\left(1-0.0051 * \beta^2\right)$ for $0<\beta<70^{\circ}$    (4)

$f=(1+0.089*h_a-0.1166*h_a*∈_p )(1+0.07866*N)$     (5)

${h_a}=5.7+3.8 *v$    (6)

The heat loss from the back surface of the collector does not exceed 10% of the heat loss from the front surface. The heat transfer coefficient of the back surface is calculated by using the following formula:

$\mathrm{U}_{\mathrm{b}}=\frac{\mathrm{k}_{\mathrm{b}}}{\mathrm{x}_{\mathrm{b}}}$    (7)

Similarly, the following formula can be used to determine the heat transfer coefficient from collector edges.

$\mathrm{U}_{\mathrm{e}}=\frac{2 * \mathrm{~L}_3\left(\mathrm{~L}_1+\mathrm{L}_2\right) \mathrm{k}_{\mathrm{i}}}{\mathrm{L}_1 \mathrm{~L}_2 \delta_{\mathrm{e}}}$    (8)

2.2 SSC heater efficiency

The SSC system efficiency ($\eta_c$) is the ratio of usable heat gain by a collector to the incident solar radiation on the absorber plate of the collector [3].

$\eta_c=\frac{Q_c}{IA_c}$    (9)

The heat gained by the collector, Q_C is calculated by multiplying the collector heat removal factor (F_R) by the possible total energy gain [10].

$\mathrm{Q}_c=\mathrm{F}_{\mathrm{R}} \mathrm{A}_{\mathrm{c}}\left[\mathrm{I}_{\mathrm{T}}(\alpha \tau)-\mathrm{U}_{\mathrm{L}}\left(\mathrm{T}_{\mathrm{wi}}-\mathrm{T}_{\mathrm{a}}\right)\right]$    (10)

Heat removal factor (F_R)

F_R= actual useful energy gain / useful energy gain if the complete collection were at fluid inlet temperature.

Mathematically can be expressed as

$\mathrm{F}_{\mathrm{R}}=\frac{\dot{\mathrm{m}} \mathrm{C}_{\mathrm{p}}}{\mathrm{A}_{\mathrm{c}} \mathrm{U}_{\mathrm{L}}}\left[1-\exp \left(-\frac{\mathrm{U}_{\mathrm{L}} \mathrm{A}_{\mathrm{c}}}{\dot{\mathrm{m}} \mathrm{Cp}}\right)\right]$    (11)

The collector plate temperature and water outlet temperature at any time interval can be given as [12]

$\mathrm{T}_{\mathrm{p}}=\mathrm{T}_{\mathrm{wi}}+\frac{\mathrm{Q}_{\mathrm{c}}}{\mathrm{A}_c \mathrm{~F}_{\mathrm{R}} \mathrm{U}_{\mathrm{I}}}\left(1-\mathrm{F}_{\mathrm{R}}\right)$    (12)

$\mathrm{T}_{\mathrm{wo}}=\frac{\mathrm{I}_{\mathrm{T}}(\mathrm{t}) *\left(\alpha \tau \mathrm{A}_{\mathrm{c}}\right)+\left(\mathrm{U}_{\mathrm{L}} * \mathrm{~A}_{\mathrm{c}}\right) *\left(\mathrm{~T}_{\mathrm{p}}-\mathrm{T}_{\mathrm{a}}\right)}{\dot{\mathrm{m}}_{\mathrm{w}} * \mathrm{C}_{\mathrm{pw}}}+\mathrm{T}_{\mathrm{wi}}$    (13)

From Eq. (11) the thermal efficiency of the collector can be reformulated as

$\eta_{\mathrm{c}}=\mathrm{F}_{\mathrm{R}}\left[\alpha * \tau-\frac{\mathrm{U}_{\mathrm{L}}\left(\mathrm{T}_{\mathrm{inl}}-\mathrm{T}_{\mathrm{a}}\right)}{\mathrm{I}_{\mathrm{T}}}\right]$    (14)

In a state where the incidence angle not (90°), a new factor known as incident angle modifier (λ_θ ) is must be added due to the change in (α*$\tau$) product will arise when (θ) not equal to (90°). For all types of flat plate collectors (k_θ) is given as [13]

$\lambda_\theta=1-b_0\left(\frac{1}{\cos \theta}-1\right)-b_1\left(\frac{1}{\cos \theta}-1\right)^2$    (15)

For a single glass collector, we can apply an equation of the first order, (b₀=0.1);

$\lambda_\theta=1-b_0\left(\frac{1}{\cos \theta}-1\right)$    (16)

Then, the final form of Eq. (14) can be calculated by using the following Eq. (14)

$\eta_{c \theta}=\mathrm{k}_\theta \mathrm{F}_{\mathrm{R}}\left\lceil\alpha_0 * \tau_0-\frac{\mathrm{U}_{\mathrm{L}}\left(\mathrm{T}_{\mathrm{inl}}-\mathrm{T}_{\mathrm{a}}\right)}{\mathrm{I}_{\mathrm{T}}}\right\rceil$    (17)

The thermal performance of SSC was verified theoretically and experimentally under the influence of different water mass flow rates in two cases. The measurements were carried out on eight days from the 25^th to the 30^th of January and on the 6^th and 7^th of March 2022. All experiments for each case were done under the same outer weather conditions in terms of beam solar radiation, ambient temperature, wind speed, and humidity, which has an obvious effect on the thermal performance of the SSC.

4.1 Open system

The variation of the outlet temperature with time for the six considered mass flow rates (0.087 to 0.025) kg/s are illustrated in Figure 4. The results were taken every (20 min) of the specified period. The results indicated that the decrease in the mass flow rate leads to an increase in the results every (20 minutes) during the designated time frame. The findings showed that a reduction in mass flow rate causes an increase in the outlet temperature. The maximum average outlet temperature reached (311 K) for a mass flow rate (0.025 kg/s) with an average inlet temperature (290 K). The increase in temperature with the lowest mass flow rate is due to more solar energy being absorbed by water through the tube wall since the water takes more time inside the spiral tube for this level of mass flow rate.

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Figure 4. Experimental outlet temperature with time

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Figure 5. Theoretical outlet temperature with time

Figure 5 describes the behavior of theoretical outlet water temperature with the variation of mass flow rate. Observations indicate that outlet temperature increases with decreasing mass flow rate, this result is very logical from an analytical point of view because the mass flow rate is in the denominator as in Eq. (13). The maximum outlet temperature reaches (328 K) at a mass flow rate (0.025 kg/s).

For the open system case, the temperature differences (T_wo-T_wi) are increasing with decreases in mass flow rate for the two solutions results as shown in Figure 6. The results indicated that the maximum temperature difference for the experimental case is (15 K) and (38 K) for theoretical results. These results of the current SSC give a temperature difference more than that obtained in reference [9] which was (12.3 K) under similar weather conditions. In addition, the spiral tube length in their study [9] is longer with an increase of (1.5 m) compared with current work and extra five coil turns. For the daily time from 11:00 to 14:30, the water mass flow rate increases up to (0.075 kg/s). As the water flows through the tube quickly, the findings are not very satisfactory. Additionally, it is not properly catching up with the heat transfer and heating it, it is the main reason why the temperature difference is less than 10 K. for a mass flow rate above (0.075 kg/s).

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Figure 6. Water temperature difference with mass flow rate

Figure 7 describes the behavior of the instantaneous efficiency of SSC with the variation of mass flow rate. Observed data show that for open system cases, the efficiency increases as the water mass flow rate increases. The maximum collector efficiency reaches more than (73%) between (11:50 to 13:50) for all ranges of mass flow rate. Increasing the intensity of radiation improves thermal efficiency. For maximum instantaneous efficiency, optimal solar beam radiation lies within the range of (975-1040) W/m². The curves before and after this period decrease in thermal efficiency due to convective and radiative losses are increased compared to useful gain energy from incident solar radiation. By comparing the obtained thermal efficiency from the current SSC with the developed spiral collector in [6] under the same mass flow rate and solar beam radiation, it is found that there is about 12% enhancement in the thermal efficiency, which is 73.16% for current SSC and 61.35% for reference [6]. The useful heat gain by water through SSC is shown in Figure 8, which indicates that the useful heat gain increases with increasing water mass flow rate. This behavior enhances the idea of increases in efficiency as shown in Figure 7. At steady state condition of water flow reaches inside the spiral tube, due to the curvature effect produces centripetal force. This type of centripetal action causes water to flow with induced force on the internal surface of the spiral tube, thus will increase the heat transfer to the water. Furthermore, the increase in water flow rate increases the velocity of water which leads to an increase in the heat transfer coefficient causing more energy to be added to the working fluid. The results were plotted in Figure 8, where the highest values of useful heat gain were recorded in the period (11:00 to 13:00) due to high beam solar radiation in this period. Figures 6-8 indicates that when it is required high outlet temperatures in industrial or residential home applications the mass flow rate must be limited between (0.025 to 0.75 kg/s). But if it is required to store an amount of energy for further use, then the specific mass flow rate is greater than (0.075 kg/s).

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Figure 7. Instantaneous efficiency for different mass flow rates

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Figure 8. Useful heat gain with time

In the case of the open system, as shown in Figure 9, the maximum temperature difference between experimental and theoretical analysis along the period of each mass flow rate is observed. It shows that the maximum difference (18.55 K) at (0.025 kg/s) is increased with decreasing the mass flow rate.

This result is due to the maximum outlet temperatures recorded in this level of mass flow rate, also the results of the highest error value were plotted corresponding to this level of mass flow rate is about (6%), then the values of percentage errors begin to decrease as the mass flow rate increases with acceptable values.

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Figure 9. The maximum temperature difference and maximum errors percentage with the mass flow rate

4.2 Closed system

The run of SSC on the (6th and 7th of March 2022) was executed with two different water mass flow rates (0.222 and 0.207) kg/s from (11:00 to 14:50) the results were taken every (5 min) of the specified period. It is clear from Figure 10 that the outlet water temperature of the two rates of the mass flow increased with time as the beam solar radiation increased with time and settle above (900 W/m²) for all periods. Due to this highest value of solar beam, the outlet temperature increases with time during this period. Small temperature differences were observed between theoretical and experimental. For the first level of mass flow rate the maximum difference was (1.24 K) and for the second level was (9.94 K). Moreover, the inlet temperature in the closed system was not constant with time in contrast to the open system. For this reason, the water outlet temperature keeps rising continuously with time for solar beam over (900 W/m²) as observed in Figure 10.

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Figure 10. Outlet temperature and solar radiation with time

Figure 11 describes the theoretical outlet temperatures with time for variation of water mass flow rate. After demonstrating a good agreement for the two levels of mass flow rate in Figure 10, the simulation of new values can be applied in a closed system case. The behavior of curves is clear from the figure since the outlet temperatures were increased with decreasing mass flow rate, this is due to the same reasons that were mentioned in the case of the open system. Another reason is added to them, which is the increase in the degree of inlet water temperature through the process of circulation in a closed system.

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Figure 11. Theoretical outlet temperature for variations mass flow rate

4.3 Validation test

Experimental results are validated theoretically, for the open system case Figure 6 showed that. The maximum error percentage that can be reached for outlet temperature between experimental and theoretical results are not exceeded 6% for all levels of mass flow rate. This result gives a good agreement between the two solutions analysis. Also, this agreement indicates the best assignment for the validation of instrument measurements. Figure 12 shows the maximum error percentage for (0.207 kg/s) mass flow rate in the closed system not exceeding 3% and for (0.2222 kg/s) mass flow rate about (0.35%). The percentage of error generated in the closed system ensures the reliability of the results for the practical and theoretical solutions.

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Figure 12. Errors percentage and temperature difference

Figure 13 shows the instantaneous efficiency of our work with reference [6] for the same mass flow rate, current work gives superiority over other work but meets at the point where maximum beam solar radiation. Our work gives stable efficiency through the period of maximum beam solar radiation than the other works. Also, the present work agrees with reference [6] about the SSC having more efficiency than the conventional type (FPSC).

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Figure 13. Instantaneous efficiency compression