3.1. Effect of the Sunlight Incident Angle θ
To study the induced propagation and collection process of sunlight changes by the effect of the θ, we compare the optical performance index of the system when the δ is 0°, 8°, 16°, and 23.45° respectively, simulated under the f = 650 mm, αab = 0.85 and ρr = 0.85. In sun tracking, the change of the ω will also affect the propagation and collection of sunlight inside the cavity absorber. To monitor the optical performance index changes of the system during the sun tracking, we simulated the case of different ω and different δ.
Figure 5a shows the effect of the
θ on the optical performance of the FLSCS using LTCR. The
ηre-opt,loss is basically unchanged for
ω of 0–30° and linearly increases for
ω of 30–60°, when the
δ = 0°. The
ηre-opt,loss are 2.25%, 2.72%, and 12.69%, respectively, when the
ω is 0°, 30°, 60°. A similar change in the
ηre-opt,loss can be seen in
Figure 5a, when the
δ = 8°. Noted that the
ηre-opt,loss are 2.62%, 3.26%, and 12.85%, respectively, when the
ω is 0°, 30°, and 60°. It means that the increases of
δ in the range of 0–8° have a weak effect on the
ηre-opt,loss. However, as shown in
Figure 5a, when the
δ is 16° and 23.45°, the
ηre-opt,loss increases as
ω raises in the range of 0–60°, and the rate of increase becomes ever larger. When the
δ is 16° and 23.45° and the
ω is 0°, 30°, and 60°, the
ηre-opt,loss are 2.94%, 4.69%, 23.1% and 4.68%, 14.43%, 41.73%, respectively. The maximum
ηre-opt,loss of the latter is basically twice that of the former. It is mainly due to the upward movement of the focus line as the
ω increases.
Figure 6 shows the upward movement distance of the focal line with the
θ. It can be seen that the focal line moves slowly upward for
δ of 0–8° and rises sharply for
δ of 8–23.45°.
To clearly observe the influence of the
δ and
ω on the propagation of sunlight, we analyze the propagation of sunlight within twice-intercepted by the cavity absorber through the simple diagram in
Figure 7. The upward movement distance for
δ = 8° is 10.7 mm, and the analysis is carried out with reference to
Figure 7d–i. It reveals that the sunlight did not escape during the two interception processes of the cavity absorber for
ω of 0–30°. Still, part of the first reflected sunlight escapes from the cavity absorber after
ω = 30°, when
δ is in the range of 0–8°. The upward movement distance for
δ = 16° is 46.7 mm, and the analysis is carried out with reference to
Figure 7a–c. It is inferred that part of the first reflected sunlight escapes from the cavity absorber for
ω of 30–60° and even part of the incident sunlight fails to be intercepted by the cavity absorber and escapes directly as
ω = 60°. The number of escaped first reflected sunlight increases with the increasing of
ω and
δ for
δ of 16–23.45°. Therefore, in addition to the cosine loss caused by the
δ, the existence of the above-mentioned escape sunlight exacerbates the increase in the
ηre-opt,loss.
Moreover, as shown in
Figure 5a, the
Xmax is increasing for
ω of 0–60°, but the growth rate of
Xmax decreases for
δ of 0–23.45°. The
Xmax mainly depends on the energy flux distribution of first intercepted sunlight on the cavity absorber inner wall. The symmetry plane of the linear Fresnel lens and the cavity receiver inner wall form an intersection line, and Δ
f represents the distance between the intersection line and the focal line. The energy flux distribution of the focus facula shows that the energy flux density in the main facula is much higher than that in the side facula [
3,
4]. The energy flux density of the focus facula is negatively related to the distance between the focal plane and the focal line. Therefore, Δ
f is used to describe the change process of the
Xmax intuitively. The smaller the Δ
f, the greater the energy flux density value on the intersection line, the greater the
Xmax, and vice versa. It can be seen in
Figure 7a–i that when the
δ is a fixed value, the Δ
f decreases with the increase of
ω, increasing the
Xmax. With the increasing of
δ, the focal line moves upward, and the Δ
f increases, finally leading to a decrease in the growth trend of Δ
f for
ω of 0–60°, leading to a decline in the growth trend of the
Xmax. In addition, the
Xmax decreases with the increase of
δ, when the
ω is a constant value. For example, when the
δ is 0°, 8°, 16° and 23.45° and the
ω = 60°, the
Xmax are 6.461, 5.950, 4.428, and 2.773, respectively. This means that the
δ has a greater influence than the
ω on the
Xmax. In other words, the
Xmax can be reduced by moving the focal line upward. Furthermore, as shown in
Figure 5a, the
σnon is increasing for
ω of 0–60°. However, it can be seen in
Figure 7a–i that the distribution area of the twice-intercepted sunlight does not monotonously increase or decrease with the change of
ω. This means that the
Xmax is far greater than the
Xmean, thus the
σnon mainly depends on the
Xmax. Note that the growth rate of
σnon increases for
δ of 0–23.45°, while the
Xmax is the opposite. In addition, the
σnon decreases with the increase of
δ, when the
ω is a constant value. For example, when the
δ is 0°, 8°, 16°, and 23.45° and the
ω = 60°, the
σnon are 0.737, 0.715, 0.662, and 0.591, respectively. It indicates that the rate of escaped sunlight increases for
δ of 0–23.45°, resulting in a sharp drop in the
Xmean. It is consistent with the change of
ηre-opt,loss. Analysis showed that the influence of
δ on optical performance is extremely greater than that of
ω.
As in the case of the LTCR,
Figure 5b shows the effect of
θ on the optical performance of the FLSCS using LACR. As shown in
Figure 5b, the
ηre-opt,loss decrease slowly for
ω of 0–15° and decreases significantly for
ω of 15–60°, when the
δ = 0°. The
ηre-opt,loss are 14.99%, 14.72%, and 2.61%, respectively, when the
ω is 0°, 15°, and 60°. Referring to
Figure 8g–i, the first intercepted sunlight escapes completely after being reflected as
ω = 0°. After that, part of the first reflected sunlight is intercepted for the second time by the cavity absorber and the number of second intercepted sunlight also increases with the
ω. A similar change in the
ηre-opt,loss can be seen in
Figure 5b, when the
δ = 8°. Noted that the
ηre-opt,loss is 15.12%, 14.33%, and 3.89%, respectively, when the
ω is 0°, 15°, and 60°. This means that the increase of
δ in the range of 0–8° has a weak effect on the
ηre-opt,loss.
However, the
ηre-opt,loss decreases for
ω of 0–45° and increases for
ω of 45–60° when the
δ = 16°, as shown in
Figure 5b. When the
ω is 0°, 45°, and 60°, the
ηre-opt,loss is 12.20%, 9.28%, and 18.03%, respectively. Referring to
Figure 8a–c, part of the first reflected sunlight escapes after being reflected as
ω = 0°. After that increases with the
ω, the number of escaped first reflected sunlight decreases, but part of the incident sunlight is blocked by the cavity absorber, increasing optical loss. It is worth noting that the
ηre-opt,loss increases for
ω of 0–60° and the growth rate of
ηre-opt,loss increases with
ω, when the
δ = 23.45°, as shown in
Figure 5b. The
ηre-opt,loss is 10.19%, 17.48%, and 40.53%, respectively, when the
ω = 0°, 30°, 60°. Referring to
Figure 8a–i, it can be inferred that the upward movement distance of the focal line is 97.2 mm as
δ = 23.45°, causing the incident sunlight not to be completely intercepted by the cavity absorber and escape. With the increasing of
ω, the number of escaped incident sunlight increases. This means that the
ηre-opt,loss mainly depends on the first intercepted sunlight.
Moreover, as shown in
Figure 5b, the
Xmax increases for
ω of 0–45° but decreases for
ω of 45–60°. Referring to
Figure 8a–i, it can be seen that the Δ
f decreases during the tracking of
ω, increasing the
Xmax of the energy flux distribution of the first intercepted sunlight. The secondary intercepted sunlight is reflected again to the distribution area of the first intercepted sunlight, resulting in the
Xmax being further increased for
ω of 0–45°. However, the distribution area of the third intercepted sunlight gradually deviates from that of the first intercepted sunlight for
ω of 45–60°, which can cause the
Xmax to decrease. Even though the focal line continues to approach the cavity absorber inner wall during the tracking of
ω and the
Xmax increases, it is not enough to compensate for the decrease in the
Xmax caused by the deviation of the secondary reflected sunlight, which ultimately leads to a decrease in the
Xmax. The
Xmax mainly depends on the energy flux distribution of first intercepted sunlight, but the energy flux distribution of the subsequently intercepted sunlight can also affect the
Xmax.
Furthermore, as shown in
Figure 5b, the
σnon increases for
ω of 0–45° and decreases for
ω of 45–60° when
δ = 0° and 8°, which is similar to the change in the
Xmax. However, it can be seen in
Figure 8d–i that the distribution area of the twice-intercepted sunlight increased for
ω of 0–60°. This means that the
Xmax is far greater than the
Xmean, thus the
σnon mainly depends on the
Xmax. Noted that the
σnon increases for
ω of 0–60° when
δ = 16° and 23.45°, as shown in
Figure 5b, which is different from the previous two cases. The growth rate of
σnon increases for
δ of 16–23.45°. It can be seen in
Figure 8c that part of the incident sunlight failed to be intercepted by the cavity absorber for the first time as
ω = 60°, resulting in a decrease in the
Xmean. The
Xmax and
σnon decrease and increase respectively for
ω of 45–60°, which means that the incident sunlight failed to be intercepted by the cavity absorber has a greater impact on the
Xmean than the
Xmax. As the
δ increases, the number of incident sunlight that fails to be intercepted by the cavity absorber increases, making the effects mentioned above more apparent.
Figure 5c shows the effect of the
θ on the optical performance of the LFR using LRCR. As shown in
Figure 5c, when the
δ = 0°, the
ηre-opt,loss decreases slowly for
ω of 0–15°, then decreases sharply for
ω of 15–45°, and finally decreases slowly for
ω of 45–60°. The
ηre-opt,loss are 15.19%, 2.80%, and 2.47%, respectively, when the
ω is 0°, 45°, and 60°. A similar change in the
ηre-opt,loss can be seen in
Figure 5c, when the
δ = 8°. Note that the
ηre-opt,loss is 15.42%, 3.66%, and 2.94%, respectively, when the
ω is 0°, 45°, and 60°. This means that the increases of
δ in the range of 0–8° have a weak effect on the
ηre-opt,loss. However, as shown in
Figure 5c, when the
δ = 16°, the
ηre-opt,loss decreases approximately linearly for
ω of 0–45° and then increases for
ω of 45–60°. The
ηre-opt,loss are 14.09%, 5.23%, and 11.10%, respectively, when the
ω is 0°, 45°, and 60°. The upward movement distance for
δ = 16° is 46.7 mm. The analysis is carried out with reference to
Figure 9a–c. It is inferred that the number of escaped first reflected sunlight decreases for
ω of 0–45°. Part of the incident sunlight fails to be intercepted and escapes for
ω of 45–60°, and the
ηre-opt,loss rises sharply. In other words, the increased energy of second intercepted sunlight is much smaller than that of escaped incident sunlight.
As shown in
Figure 5c, when the
δ = 23.45°, the
ηre-opt,loss increases for
ω of 0–60°, and the growth rate of
ηre-opt,loss becomes ever larger. When the
ω is 0°, 30°, and 60°, the
ηre-opt,loss are 12.86%, 16.72%, and 37.75%, respectively. This is mainly due to the upward movement of the focus line as the
δ increases. The upward movement distance for
δ = 23.45° is 97.2 mm. It is more than twice that in
Figure 5c as the
δ = 16°. Thus, the
ηre-opt,loss mainly depends on the first intercepted sunlight. Moreover, as shown in
Figure 5c, the
Xmax is decreasing for
ω of 0–45° and increasing for
ω of 45–60°. The
Xmax mainly depends on the energy flux distribution of first intercepted sunlight. It can be seen in
Figure 9a–i that when the
δ is a fixed value, with increasing
ω, Δ
f have an increase, followed by a decrease, resulting in a similar change in the
Xmax. With the increasing of
δ, the focal line moves upward and the Δ
f increases, leading to a decrease in
Xmax with the rise of
δ when the
ω is a constant value. For example, when the
δ is 0°, 8° 16°, and 23.45° and the
ω = 60°, the
Xmax are 7.007, 6.144, 6.056, and 3.986 respectively. Furthermore, as shown in
Figure 5c, the
σnon is decreasing for
ω of 0–45° and increasing for
ω of 45–60°. It is consistent with the changing trend of the
Xmax. It can be seen in
Figure 9a–i that the distribution area of the twice-intercepted sunlight does not monotonously increase or decrease with the change of
ω. This means that the
Xmax is far greater than the
Xmean, thus the
σnon mainly depends on the
Xmax. In addition, the
σnon decreases with the increase of
δ for
ω of 0–45°, when the
ω is a constant value. However, the
σnon variation of
ω = 60° is not monotonous for
δ of 0–23.45°, because part of the incident sunlight fails to be intercepted and escapes.
3.2. Effect of the Receiver Position f
To investigate the effect of the
f on the optical performance more detail, four cases of
f = 600, 625, 675, and 700 mm are selected for comparative analysis during the downward and upward shift of the linear Fresnel lens. To avoid the influence of the upward movement of the focal line caused by the change of
δ, the situation of
δ = 0° is selected for analysis and simulated under the
αab = 0.85 and
ρr = 0.85, as shown in
Figure 10.
Figure 10a shows the effect of the
f on the optical performance of the FLSCS using LTCR. As shown in
Figure 10a, the
ηre-opt,loss is basically unchanged for
ω of 0–30° and increases for
ω of 30–60° when the
f = 600 mm and 625 mm. However, the difference from the change in
Figure 5a of
δ = 0° is that the growth rate of
ηre-opt,loss increases for
ω of 30–60°. When the
f is 600 mm, 625 mm and the
ω is 30°, 45°, and 60°, the
ηre-opt,loss are 2.25%, 5.81%, 24.16%, and 2.25%, 6.65%, 14.92%, respectively. It means that the
ηre-opt,loss decreases as
f decreases for
ω of 0–45°, but the
ηre-opt,loss increases as
f decreases when
ω = 60°. The downward shift of the linear Fresnel lens can be referenced in
Figure 7j–o. It reveals that the sunlight is completely intercepted by the cavity absorber twice for
ω of 0–45°, and more of the secondary reflected sunlight is intercepted by the cavity absorber again, resulting in a decrease in the
ηre-opt,loss. However, part of the incident sunlight may be blocked by the cavity absorber before entering when the
ω = 60°, and the optical blocking loss becomes more serious as
f decreases. As shown in
Figure 10a, the
ηre-opt,loss increases for
ω of 0–60° when the
f = 675 mm and 700 mm. However, the difference from the change in
Figure 5a of
f = 650 mm is that the
ηre-opt,loss increases for
ω of 0–30°. When the
f is 675 mm, 700 mm and the
ω is 0°, 30°, the
ηre-opt,loss are 2.25%, 2.91% and 2.25%, 3.83% respectively. It means that the
ηre-opt,loss remains substantially unchanged with the
f of 600–700 mm as
δ = 0° and
ω = 0°, but the
ηre-opt,loss increases for
f of 650–700 mm as
δ = 0° and
ω = 30°. The upward shift of the linear Fresnel lens can be referenced to
Figure 7a–f. It reveals that when the
ω = 0°, the sunlight is completely intercepted by the cavity absorber twice, and when the
ω = 30°, part of the first reflected sunlight escapes from the cavity absorber, becoming more obvious as
f increases.
Moreover, different from the change of the
Xmax in
Figure 5a of
f = 650 mm, the
Xmax of
f = 600 mm increases first and then decreases with the increase of
ω, and the situation change occurs as the
ω = 30°. Referring to
Figure 7m–o, it can be seen that the focal line first approaches the cavity absorber inner wall and then moves away from it during the tracking of
ω. Combined with the changing trend of
Xmax in
Figure 10a as the
f = 600 mm, it can be seen that the
Xmax reaches its maximum value when the focal line falls on the cavity absorber inner wall, and the corresponding
ω is in the range of 15° to 30°. The changing trend of
Xmax as
f = 625, 675, and 700 mm is similar to that of
f = 650 mm, the
Xmax increase for
ω of 0–60°. Referring to
Figure 7a–f,j–l, it can be seen that the Δ
f decreases during the tracking of
ω. With the increasing of
ω, part of the first reflected sunlight escapes from the cavity absorber. The number of second reflected sunlight reflected to the distribution area of the first intercepted sunlight decreases. This would originally cause the
Xmax to decrease. Still, the actual
Xmax increases with the increase of
ω, which indicates that the
Xmax depends on the energy flux distribution of first intercepted sunlight. Furthermore, as shown in
Figure 10a, the
σnon is increasing for
ω of 0–60°. Note that the variation of
ηre-opt,loss,
Xmax, and
σnon with the
ω and
f in
Figure 10a of
f = 625 mm, 675 mm and 700 mm are similar to those in
Figure 5a of
δ = 16° and 23.45°, and thus detailed analysis is omitted herein. However, the changing trend of
σnon in
Figure 10a as the
f = 600 mm is inconsistent with that of the
Xmax for
ω of 30–60°. It shows that the decrease rate of
Xmean is much greater than that of
Xmax; that is, the influence of optical blocking loss on the
Xmean is greater than the
Xmax as
f = 600 mm. In addition, except for the
σnon of the
ω = 45° and 60° as
f = 600 mm, the
σnon decreases with the increase of
f when the
ω is a constant value. For example, when the
f is 600 mm, 625 mm, 675 mm, and 700 mm as the
ω = 0°, the
σnon is 0.527, 0.501, 0.413, and 0.346, respectively. Referring to
Figure 7a–o, it can be seen that the distribution area of the incident sunlight intercepted by the cavity absorber for the first time increases for
f of 600–700 mm when the
ω is a constant value, resulting in a drop in the
σnon.
As in the case of the LTCR,
Figure 10b shows the effect of
f on the optical performance of the FLSCS using LACR. As shown in
Figure 10b, when the
f = 600 mm and 625 mm, the
ηre-opt,loss is basically unchanged for
ω of 0–15°, then decreases for
ω of 15–45° and finally increased for
ω of 45–60°. However, the difference from the change in
Figure 5b of
δ = 0° is that the of
ηre-opt,loss increases for
ω of 45–60°. When the
f = 600 mm and 625 mm and the
ω = 45° and 60°, the
ηre-opt,loss are 6.04%, 13.18% and 3.37%, 3.55% respectively. It means that the
ηre-opt,loss increases as
f decreases for
ω of 45–60°. The downward shift of the linear Fresnel lens can be referenced in
Figure 8l,o. It reveals that with the decreasing of
f, part of the incident sunlight may be blocked by the cavity absorber before entering for
ω of 45–60°, and the optical blocking loss becomes more severe as
f decreases.
Figure 10b of the
f = 675 mm shows that the
ηre-opt,loss decreases for
ω of 0–60°. It is similar to the change of
ηre-opt,loss in
Figure 5b of
δ = 0°. Nevertheless, the
ηre-opt,loss decreased for
ω of 0–45° and increased for
ω of 45–60° in
Figure 10b as
f = 700 mm. When the
f = 675 mm and 700 mm and the
ω = 45° and 60°, the
ηre-opt,loss are 7.26%, 6.29% and 8.33%, 16.65%, respectively. Referring to
Figure 8a–f, it can be seen that with the increase of
ω, the number of escaped first intercepted sunlight gradually decreases, thus the
ηre-opt,loss decreases. However, with the increase of
f, the spatial distribution area of the light after passing the focal line increases. Part of the incident sunlight failed to be intercepted by the cavity absorber for the first time as
ω = 60°, increasing the
ηre-opt,loss. Note that the
ηre-opt,loss decreases as
f increases for
ω of 0–30°. The distribution area of first intercepted sunlight increases as
f increases, increasing the number of second intercepted sunlight, and thus the
ηre-opt,loss decreases.
Moreover, the changing trend of
Xmax as
f = 600, 625, 675, and 700 mm in
Figure 10b is similar to that of
f = 650 mm in
Figure 5b as
δ = 0°, the
Xmax increase for
ω of 0–45° and decreases for
ω of 45–60°. Thus, detailed analysis is omitted herein. The
Xmax should generally increase as
f decreases when the
ω is fixed. However, when the
f = 600, 625, 675, and 700 mm and the
ω = 45°, 60°, the
Xmax are 7.477, 7.626, 6.740, 5.912 and 5.832, 6.949, 6.509, 5.699, respectively. Referring to
Figure 8m–o, it can be seen that when
f = 600 mm, the trajectory of the focal line intersects with the LACR, causing the focal line to approach and then move away from the cavity absorber inner wall during the tracking of
ω, thus the
Xmax decrease as the
ω = 45°, 60° for the
f = 600 mm and 625 mm. Furthermore, as shown in
Figure 10b, when the
f = 600 mm, the
σnon is unchanged for
ω of 0–15°, then decreases for
ω of 15–60°. It is inconsistent with the change of the
Xmax. Referring to
Figure 8m–o, it can be seen that the distribution area of the twice-intercepted sunlight increased for
ω of 0–60°. In addition, the
ηre-opt,loss decreases for
ω of 0–45° and increase for
ω of 45–60°. Thus, the
Xmean has a greater impact on the
σnon than that of the
Xmax for
ω of 0–45°, and the situation is reversed for
ω of 45–60°. As shown in
Figure 10b, when the
f = 625 mm, the
σnon increase for
ω of 0–30°, then decrease for
ω of 30–60°. It is consistent with the change of the
Xmax for
ω of 0–30°. This is because the
ηre-opt,loss is almost unchanged for
ω of 0–30°, thus the
Xmean basically unchanged. However, the
ηre-opt,loss drops sharply for
ω of 30–45°, while the
Xmax rises sharply. It means that the
Xmean has a greater impact on the
σnon than the
Xmax for
ω of 30–45°. Noted that the
Xmean almost unchanged for
ω of 45–60° due to the stable
ηre-opt,loss. Therefore, the change of
σnon depends on that of
Xmax. As shown in
Figure 10b, when the
f = 675 mm, the
σnon increase for
ω of 0–45°, then decrease for
ω of 45–60°. It is consistent with the change of the
Xmax for
ω of 0–60°, and the
ηre-opt,loss decrease for
ω of 0–60°. It means that the
Xmax has a greater impact on the
σnon than the
Xmean for
ω of 0–60°. A similar situation can be seen in
Figure 10b as the
f = 700 mm for
ω of 0–45°. However, the
σnon and
ηre-opt,loss increase for
ω of 45–60° during the
Xmax decrease. It means that the
Xmean has a greater impact on the
σnon than the
Xmax for
ω of 45–60°.
Figure 10c shows the effect of the
f on the optical performance of the LFR using LRCR. As shown in
Figure 10c, when the
f = 600 mm and 625 mm, the
ηre-opt,loss decreases slowly for
ω of 0–15°, then drops sharply for
ω of 15–45°, and finally increases for
ω of 45–60°. However, the difference from the change in
Figure 5c of
f = 650 mm as
δ = 0° is that the
ηre-opt,loss increases for
ω of 45–60°. When the
f is 600 mm, 625 mm and the
ω is 0°, 45°, and 60°, the
ηre-opt,loss are 15%, 2.8%, 16.72% and 15%, 2.26%, 5.48%, respectively. It means that the change of
f has a weak influence on the
ηre-opt,loss for
ω of 0–45°. The downward shift of the linear Fresnel lens can be referenced in
Figure 9j–o. It reveals that in tracking the
ω, the distribution area of first intercepted sunlight is concentrated on the bottom, then on the bottom and one side, and finally on one side of it. The distribution area of the first intercepted sunlight is concentrated on the bottom, and one side increases the number of the reflection of sunlight and reduces the number of escaped secondary reflected sunlight, which is similar to the role of an LTCR. The sharp increase in the
ηre-opt,loss of
f = 600 mm as the
ω = 60° is due to part of the incident sunlight being blocked by the cavity absorber before entering, and the optical blocking loss becomes more serious as
f decreases. As shown in
Figure 10c, when the
f = 675 mm and 700 mm, except for the
ηre-opt,loss of
f = 700 mm as the
ω = 60°, the
ηre-opt,loss decreases with the increasing of
ω. It is similar to the change of the
ηre-opt,loss in
Figure 5c of
f = 650 mm as
δ = 0°. When the
f is 675 mm, 700 mm and the
ω is 0°, 30°, 60°, the
ηre-opt,loss are 15%, 6.64%, 3.17% and 14.43%, 8.15%, 9.74, respectively. The upward shift of the linear Fresnel lens can be referenced in
Figure 9a–f. It reveals that the number of second intercepted sunlight increases with the increase of
f for
ω of 0–15°, but the number of incident sunlight which fails to be intercepted and escapes increases with the increase of
f for
ω of 15–60°. Moreover, the change of the
Xmax in
Figure 10c is similar to that in
Figure 5c of
f = 650 mm as
δ = 0°, the
Xmax decreases for
ω of 0–45° and then decreases for
ω of 45–60°. It can be seen in
Figure 9a–i that when the
ω is a fixed value, Δ
f increases with the increasing of
f, resulting in a similar change in the
Xmax. For example, when the
f = 600, 625, 675 and 700 mm and the
ω is 60°, the
Xmax are 8.341, 8.686, 5.514 and 4.395, respectively. Furthermore, as shown in
Figure 10c, the
σnon decreases for
ω of 0–45° and then decreases for
ω of 45–60°. The changing trend of
σnon is consistent with the
Xmax for
ω of 0–60°. In addition, the
σnon decreases with the increase of
f, when the
ω is a constant value. For example, when the
f is 600, 625, 675 and 700 mm as the
ω = 0°, the
σnon are 0.832, 0.828, 0.747 and 0.671 respectively. Referring to
Figure 9a–o, it can be seen that the distribution area of twice-intercepted sunlight increases for
f of 600–700 mm when the
ω is a constant value, resulting in a drop in the
σnon.
3.3. Effect of Receiver Internal Surface Absorptivity αab
After the specific case study, the parametric study was conducted to quantify the effects of
αab on the optical performance of the system. The existence of
δ causes the sunlight to obliquely enter the linear Fresnel lens and then move the focal line upwards, which leads to a decrease in the number of rays intercepted by the cavity absorber. Therefore, the
αab has a great influence on the
ηre-opt,loss. In addition, the reflection number of sunlight inside the cavity absorber is also greatly affected by the
αab, which ultimately affects the
σnon, especially when the
δ = 23.45°. In this section, for the receiver internal surfaces, three kinds of
αab (0.75, 0.85, and 1.00) were considered, and the
ω varying from 0° to 60° at the particular
αab was numerically analyzed under the
f = 650 mm (except for LACR) and
ρr = 0.85.
Figure 11a shows the effect of the
αab on the optical performance of the FLSCS using LTCR.As shown in
Figure 11a, the
ηre-opt,loss increases with the decrease of
αab, but its increasing trend gradually decreases with the increase of
ω. For example, when the
ω = 0° and 60°, the
αab is 1.00, 0.85, and 0.75, the
ηre-opt,loss is 2.47%, 4.68%, 6.32% and 35.56%, 41.73%, 46.53%, respectively. Referring to
Figure 7a–c, as the
ω increases, the distribution area of first intercepted sunlight gradually moves from two sides to one side, resulting in a gradual decrease in the number of secondary intercepted sunlight. Thus, the absorbed sunlight energy is increasingly dependent on the first interception, and the ratio of
ηre-opt,loss is close to the ratio of
αab when the
ω = 60°. In other words, the cavity structure can be optimized to increase the number of incident sunlight reflections on the inner wall, thereby reducing the requirement for high
αab. Moreover, as shown in
Figure 11a, the
Xmax increases with the decrease of
αab as the
ω = 0°, while the
Xmax decreases with the decrease of
αab for
ω of 15–60°. In addition, the decreasing trend of
Xmax with the
αab becomes more obvious for
ω of 15–60°. This is because the incident sunlight is symmetrically distributed on both bottom sides of the cavity absorber when the
ω = 0°. With the decreasing of
αab, the number of the reflection of the sunlight on both bottom sides increases to form energy accumulation, increasing
Xmax. Referring to
Figure 7a–c, as the
ω increases, the distribution area of first intercepted sunlight gradually shifts to one side, part of the second reflected sunlight escapes, and the energy-concentration effect decreases. The
Xmax mainly depends on the energy flux distribution of the first intercepted sunlight. The greater the
αab, the greater the
Xmax. The Δ
f decreases with the increase of
ω, thus the energy flux density of first intercepted sunlight increases, resulting in a more noticeable difference in
Xmax with different
αab. As shown in
Figure 11a, the variation of
σnon is similar to that of the
Xmax. The
σnon increases with the decrease of
αab as the
ω = 0°, and the situation is the opposite for
ω of 15–60°. It further shows that the
Xmax is far greater than the
Xmean, and the
σnon mainly depends on the
Xmax. However, unlike the change of
Xmax, the decreasing trend of
σnon with the
αab becomes gentle as
ω increases in the range of 15–60°. This is because as the
ω increases, the energy absorbed of first intercepted sunlight accounts for an increasing proportion of the total absorbed energy. In other words, the energy flux distribution mainly depends on the distribution of first intercepted sunlight. Therefore, the influence of
αab on the
σnon is weakened.
As in the case of the LTCR,
Figure 11b shows the effect of
αab on the optical performance of the FLSCS using LACR. To avoid being affected by the occluded and escaped incident sunlight, the case of
f = 675 mm is selected. As shown in
Figure 11b, the
ηre-opt,loss increases with the decrease of
αab, but its increasing trend gradually decreases with the increase of
ω. For example, when the
ω = 0° and 60°, the
αab is 1.00, 0.85, and 0.75, the
ηre-opt,loss is 12.75%, 19.11%, 23.71% and 48.27%, 52.44%, 55.61%, respectively. Since the upward movement distance of focal line is 97.2 mm as
δ = 23.45° and the
f = 675 mm, referring to
Figure 8a–c, as the
ω increases, the distribution area of first intercepted sunlight gradually moves from the bottom to one side, resulting in a gradual increase in the number of secondary intercepted sunlight. Therefore, as the number of the reflection of sunlight in the cavity absorber increases, the effect of
αab on the absorption of sunlight energy decreases gradually. Moreover, as shown in
Figure 11b, the
Xmax decreases with the decrease of
αab for
ω of 0–60°. In addition, the decreasing trend of
Xmax with the
αab is basically stable before
ω = 45° but becomes obvious as
ω increases in the range of 45–60°. Referring to
Figure 8a–c, it can be inferred that the energy flux distribution mainly depends on the first intercepted sunlight, and with the increase of
ω, there is an increase in the amount of escaped sunlight. Therefore, the influence of
αab on the
Xmax is intensified, and the amount of escaped sunlight increases sharply for
ω of 45–60°. When the
ω = 60°, the
αab is 1.00, 0.85 and 0.75, the
Xmax is 4.782, 4.034, 3.567, respectively, which is close to the ratio between the different
αab. As shown in
Figure 11b, the variation of
σnon is similar to that of the
Xmax. The
σnon decreases with the decrease of
αab. Before
ω = 45°, the variation of the
σnon with the
αab can basically be ignored, but it becomes obvious as
ω increases in the range of 45–60°. This is because the energy flux distribution mainly depends on the distribution of first intercepted sunlight, especially for
ω of 0–45°. Therefore, the influence of
αab on the
σnon is weakened. However, the amount of escaped sunlight increases sharply for
ω of 45–60°, the distribution of second or more intercepted sunlight has an increased influence on the energy flux distribution. When the
ω = 0° and 60°, the
αab is 1.00, 0.85, and 0.75, the
σnon is 0.4065, 0.404, 0.4016 and 0.6205, 0.5864, 0.5636, respectively.
As in the case of the LTCR,
Figure 11c shows the effect of
αab on the optical performance of the FLSCS using LRCR as
f = 650 mm. As shown in
Figure 11c, the
ηre-opt,loss increases with the decrease of
αab, but its increasing trend gradually decreases with the increase of
ω. For example, when the
ω = 0° and 60°, the
αab is 1.00, 0.85, and 0.75, the
ηre-opt,loss is 2.47%, 12.86%, 20.99% and 36.08%, 37.75%, 39.06%, respectively. Referring to
Figure 9a–c, as the
ω increases, the distribution area of first intercepted sunlight gradually moves from the bottom to one side, resulting in a gradual increase in the number of secondary intercepted sunlight. Therefore, as the number of the reflection of sunlight in the cavity absorber increases, the effect of
αab on the absorption of sunlight energy decreases gradually. Moreover, as shown in
Figure 11c, the
Xmax decreases with the decrease of
αab for
ω of 0–60°. In addition, the decreasing trend of
Xmax with the
αab decrease for
ω of 0–60°. Referring to
Figure 9a–c, it can be inferred that the energy flux distribution mainly depends on the first intercepted sunlight as
ω = 0°, and with the increase of
ω, the amount of secondary intercepted sunlight increases. Especially as
ω = 60°, part of the incident sunlight fails to be intercepted and escapes. The influence of the secondary intercepted sunlight on the energy flux distribution gradually increases. Therefore, the influence of
αab on the
Xmax decreases as the
ω increases. When the
ω = 60°, the
αab is 1.00, 0.85 and 0.75, the
Xmax is 4.221, 3.986, 3.751, respectively. As shown in
Figure 11c, the variation of
σnon is similar to that of the
Xmax. The
σnon decreases with the decrease of
αab. It further shows that the
Xmax is far greater than the
Xmean, and the
σnon mainly depends on the
Xmax. Noted that the decrease rate of
σnon presents continuous fluctuations for
ω of 0–60°. However, the increase rate of the
ηre-opt,loss and the decrease rate of the
Xmax is decreased for
ω of 0–60°. In other words, the
αab can affect the change rate of
σnon, but not the changing trend. When the
ω = 0° and 60°, the
αab is 1.00, 0.85, and 0.75, the
σnon is 0.682, 0.6663, 0.6558 and 0.7039, 0.6945, 0.6822, respectively.
3.4. Effect of End Reflection Plane Reflectivity ρr
The increase of the δ causes the light to enter the cavity absorber obliquely. The end loss can be effectively reduced by sliding the mirror element, and the sunlight reflected by the cavity absorber inner wall tends to propagate to one end. By setting the end reflection plane, the sunlight incident on the end can be reflected again so that it has a chance to be intercepted again by the cavity absorber to reduce the optical loss further. The end reflection plane itself has a role in the amount of sunlight reflected and lost. Thus, the effect of the end reflection plane in reducing the optical loss and its influence on the energy flux distribution is explained by studying end reflection planes with different ρr. In this section, for the end reflection planes, three kinds of ρr (0.75, 0.85 and 1.00) were considered, and the ω varying from 0° to 60° at the particular ρr was numerically analyzed. The f, αab and δ are 650 mm, 0.85, and 23.45°, respectively.
Figure 12a shows the effect of the
ρr on the optical performance of the FLSCS using LTCR. It can be seen from
Figure 12a that the
ηre-opt,loss increases slightly as the
ρr decreases when the
ω is fixed. The average
ηre-opt,loss for
ρr = 1.00, 0.85, and 0.75 are 18.49%, 18.56%, and 18.60%, respectively, for
ω of 0–60°. However, the average
ηre-opt,loss is reduced by 0.46%, 0.39%, and 0.35%, respectively, compared to 18.95% if the end reflection plane is not installed. It can be inferred that the number of incident sunlight on the end reflection plane can be ignored compared to intercepted sunlight. The results prove that sliding the lens element can effectively solve the problem of end loss. In addition, as shown in
Figure 12a, the
Xmax decreases with the decrease of
ρr for
ω of 0–60°. It is because part of the incident sunlight on the end reflection plane is reflected on the cavity absorber inner wall again, which causes the
Xmax to increase. However, the sunlight mentioned above energy decreases as the
ρr decreases, decreasing the
Xmax. The average
Xmax for
ρr = 1.00, 0.85, and 0.75 are 2.629, 2.586, and 2.565, respectively, for
ω of 0–60°. The average
Xmax is increased by 3.91%, 2.21%, and 1.38%, respectively, compared to 2.531 if the end reflection plane is not installed. As shown in
Figure 12a, the variation of
σnon with
ρr is similar to that of the
Xmax. The
σnon decreases with the decrease of the
ρr for
ω of 0–60°. It is because the
ηre-opt,loss of different
ρr is almost constant for
ω of 0–60°, resulting in a similar
Xmean; thus, the
σnon depends on the
Xmax. The average
σnon for
ρr = 1.00, 0.85, and 0.75 are 0.385, 0.372, and 0.366, respectively, for
ω of 0–60°. The average
σnon is increased by 7.84%, 4.20%, and 2.52%, respectively, compared to 0.357 if the end reflection plane is not installed. This indicates that the optical loss can be slightly reduced by setting the end reflection plane. Still, compared with the cost of the end reflection plane and the increased non-uniformity of the energy flux distribution, the cost performance of setting the end reflection plane is low.
Figure 12b shows the effect of
ρr on the optical performance of the FLSCS using LACR. It can be seen from
Figure 12b that the
ηre-opt,loss increases slightly as the
ρr decreases when the
ω is fixed. The average
ηre-opt,loss at
ρr of 1.00, 0.85, and 0.75 are 31.43%, 31.55%, and 31.64%, respectively for
ω of 0–60°. It can be inferred that the number of sunlight incidents on the end reflection plane is negligible compared to the amount of intercepted sunlight by the cavity absorber. In other words, the end reflection plane can be replaced by insulating cotton, which reduces the cost of the system and reduces heat loss. In addition, as shown in
Figure 12b, the
Xmax decreases with the decrease of
ρr. The changing trend of
Xmax as
f = 675 mm using LACR is similar to that of
f = 650 mm using LTCR, and thus detailed analysis is omitted herein. The average
Xmax at
ρr of 1.00, 0.85, and 0.75 are 4.755, 4.456 and 4.262, respectively for
ω of 0–60°. As shown in
Figure 12b, the variation of
σnon with
ρr is similar to that of the
Xmax. The
σnon decreases with the decrease of the
ρr for
ω of 0–60°. It is because the
ηre-opt,loss of different
ρr is almost constant, resulting in a similar
Xmean, and the
σnon depends on the
Xmax. The average
σnon at
ρr of 1.00, 0.85, and 0.75 are 0.498, 0.465, and 0.441, respectively, for
ω of 0–60°. This indicates that the effect of setting the end reflection plane on the optical efficiency of the system is negligible, and it will increase the hot spot effect on the cavity receiver inner wall.
Figure 12c shows the effect of
ρr on the optical performance of the FLSCS using LRCR. It can be seen from
Figure 12c that the
ηre-opt,loss increases slightly as the
ρr decreases when the
ω is fixed. The average
ηre-opt,loss at
ρr of 1.00, 0.85, and 0.75 are 20.78%, 20.94%, and 21.04%, respectively for
ω of 0–60°. It can be inferred that the number of sunlight incidents on the end reflection plane is negligible compared to the amount of intercepted sunlight by the cavity absorber. In addition, as shown in
Figure 12c, the
Xmax decreases with the decrease of
ρr. The average
Xmax at
ρr of 1.00, 0.85, and 0.75 are 4.798, 4.459, and 4.244, respectively, for
ω of 0–60°. The average
Xmax difference of different
ρr is obvious, but the difference of average
ηre-opt,loss of that is small. As shown in
Figure 12c, the variation of
σnon with
ρr is similar to that of the
Xmax. The
σnon decreases with the decrease of the
ρr for
ω of 0–60°. It is because the
ηre-opt,loss of different
ρr is almost constant, resulting in a similar
Xmean, and the
σnon depends on the
Xmax. The average
σnon at
ρr of 1.00, 0.85, and 0.75 are 0.676, 0.652, and 0.635, respectively, for
ω of 0–60°. Therefore, introducing the end reflection plane will aggravate the non-uniformity of the energy flux distribution without significantly increasing the optical efficiency.