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Research Papers

Applicability of Heat Mirrors in Reducing Thermal Losses in Concentrating Solar Collectors PUBLIC ACCESS

[+] Author and Article Information
Vikrant Khullar

Mechanical Engineering Department,
Thapar Institute of Engineering and Technology,
Patiala 147004, Punjab, India
e-mail: vikrant.khullar@thapar.edu

Prashant Mahendra, Madhup Mittal

Mechanical Engineering Department,
Thapar Institute of Engineering and Technology,
Patiala 147004, Punjab, India

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received October 31, 2017; final manuscript received June 2, 2018; published online August 6, 2018. Assoc. Editor: Nesrin Ozalp.

J. Thermal Sci. Eng. Appl 10(6), 061004 (Aug 06, 2018) (14 pages) Paper No: TSEA-17-1422; doi: 10.1115/1.4040653 History: Received October 31, 2017; Revised June 02, 2018

In the present work, a novel parabolic trough receiver design has been proposed. The proposed design is similar to the conventional receiver design except for the envelope and the annulus part. Here, a certain portion of the conventional glass envelope is coated with Sn-In2O3 and also Sn-In2O3 coated glass baffles are provided in the annulus part to reduce the radiative losses. The optical properties of the coated glass are such that it allows most of the solar irradiance to pass through, but reflects the emitted long wavelength radiations back to the absorber tube. Sn-In2O3 coated glass is referred to as “transparent heat mirror.” Thus, effectively reducing the heat loss area and improving the thermal efficiency of the solar collector. A detailed one-dimensional steady-state heat transfer model has been developed to predict the performance of the proposed receiver design. It was observed that while maintaining the same external conditions (such as ambient/initial temperatures, wind speed, solar insolation, flow rate, and concentration ratio), the heat mirror-based parabolic trough receiver design has about 3–5% higher thermal efficiency as compared to the conventional receiver design. Furthermore, the heat transfer analysis reveals that depending on the spatial incident solar flux distribution, there is an optimum circumferential angle (θ = θoptimum, where θ is the heat mirror circumferential angle) up to which the glass envelope should be coated with Sn-In2O3. For angles higher than the optimum angle, the collector efficiency tends to decrease owing to increase in optical losses.

Parabolic trough collectors (PTC) have been widely researched with the objective of improving their performance characteristics and reducing operating (and maintenance) costs [13]. Also, a few researchers have employed machine learning techniques such as artificial neural networks to optimize the performance of these solar thermal systems [46].

Receiver or the heat collector element forms the heart of these systems; any improvement in this component could significantly enhance the overall efficiency of the parabolic trough collectors. In this direction, numerous receiver design modifications have been proposed by various researchers [713]. Figure 1 gives the details of selected receiver designs in the literature. Most of these design modifications focus on reducing the thermal losses without ensuring high optical efficiency [10] or vice versa [11]. Furthermore, most of them [1113] do not take into account the spatial distribution and spectral nature of the flux reaching the receiver.

In a typical parabolic trough design, the concentrated solar irradiance flux distribution is essentially nonuniform across the receiver circumference—only a limited portion of the receiver circumference receives concentrated solar irradiance [1417]. However, thermal losses occur across the complete circumference of the receiver. Therefore, in order to improve the efficiency of the collector, a mechanism needs to be devised to reduce the circumferential area from which thermal losses take place without hampering the optical efficiency of the system.

The present study introduces one such novel receiver design that essentially results in lower thermal losses and simultaneously ensures higher optical and hence overall efficiency relative to the parabolic trough collectors employing conventional receiver design. The Design and Constructional Details section details the basic idea and constructional details of the proposed receiver design.

Basic Design.

Figure 2(a) shows the schematic of a parabolic trough collector employing the proposed receiver design. Solar irradiance, which is incident normally on the parabolic trough aperture, is focused onto a cylindrical receiver lying along the focal axis of the parabola. Depending on the optical properties of the glass envelope, a small portion of the incident solar irradiance is reflected/absorbed by the glass envelope and rest (majority) is able to reach the selectively coated metal tube. Here, the radiant energy is converted into the thermal energy gain in the metal tube (depending on the absorptivity of the selectively coated metal tube). Finally, the thermal energy in the metal tube is transferred to the working fluid primarily through convection mechanism.

The proposed receiver design is similar to the conventional receiver design (see Fig. 2(b)) except for the envelope part. Here, some portion of the low iron glass envelope is coated with Sn-In2O3 (see Fig. 2(c)). Therefore, the envelope could be thought of as made up of two parts: uncoated and the coated part. The uncoated part being made up of low-iron glass has high transmittance in the incident solar irradiance wavelength band and high emittance in the midinfrared region. On the other hand, the coated part has relatively lower transmittance in the incident solar irradiance wavelength band (but at the same time has high reflectance in the midinfrared region). Thus, the two aforesaid characteristics can be exploited to make a sort of hybrid envelope having coated and uncoated regions depending upon the solar irradiance flux distribution around the receiver.

This design shall ensure reduction in radiative losses (especially at high receiver tube temperatures) without significantly affecting the optical efficiency of the system. It may be noted that the two portions of the glass are separated by elements (Sn-In2O3 coated glass baffles), which are highly reflective in the infrared (IR) region; the sole purpose of these is to prevent the infiltration of IR radiation (i.e., there is no direct radiative heat transfer) between the uncoated and coated portions of the glass envelope.

It may also be noted that due to beam broadening, tracking inaccuracies, and mirror surface defects, it could be really difficult to ensure normal incidence of solar irradiance and in that event, the baffles may actually hinder the incident solar irradiance.

In the case of the conventional receiver design, optical losses are inherently low owing to the usage of low-iron glass envelope. However, in the proposed receiver design, optical losses increase with increase in the circumferential heat mirror angle. But at the same time, the radiation losses dip down significantly, especially at high temperatures. The spatial flux distribution around the receiver dictates the region of the glass envelope, which needs to be coated with Sn-In2O3 so that thermal losses could be significantly reduced without hampering the optical efficiency of the collector.

Geometrical Details.

In order to quantitatively evaluate the performance of the proposed receiver design and to aid comparison, the dimensions of the proposed novel parabolic trough design have been kept similar to that of (Solar Electric Generating System) SEGS LS-2 collector [17,18]. LS2 collector design has been chosen as it is the most famous (extensively researched) collector design and nearly accounts for the 65% of the collectors installed in SEGS power plants in California [19].

Table 1 details the geometrical properties of various components of the parabolic trough.

Optical Properties.

As noted earlier, the proposed receiver design differs from the conventional receiver essentially in terms of the glass envelope optical properties; here, some portion of the glass envelope is coated with Sn-In2O3. In the present work, the optical properties (spectral reflectance and transmittance) of the Sn-In2O3 coated portion of the glass envelope and the coated baffles have been approximated by Drude free-carrier model.

In order to accomplish the aforementioned task, the spectral optical constants, i.e., index of refraction and index of absorption, need to be found. The photon-energy dependence of the complex dielectric constant) of coatings on glass (such as Sn-In2O3 in the present study could be accurately approximated by Drude free-carrier model [2123], mathematically expressed as Display Formula

(1)nh,λ2κh,λ2=εEp2Eλ2+Ec2
Display Formula
(2)2nh,λκh,λ=EcEp2Eλ(Eλ2+Ec2)

where nh,λ and κh,λ are the spectral indices of refraction and absorption (also called spectral optical constants) of the heat mirror (coated portion of the glass envelope); ε is the adjustment parameter (a constant across the spectral region of interest); and Ep, Ec, Eλ are the plasma, relaxation, and spectral photon energies, respectively. Fan and Bachner [21] have experimentally determined the values of the adjustment parameter, plasma energy, and relaxation energy for Sn-In2O3 coated glass substrates. Therefore, in the present work, the values reported in Ref. [21] have been used to calculate the spectral optical constants.

Once the spectral optical constants are known, the effective spectral reflectance could be evaluated Display Formula

(3),λ=(nacosψu)2+v2(nacosψ+u)2+v2
Display Formula
(4),λ=[(nh,λ2κh,λ2)cosψnau]2+[2nh,λκh,λcosψnav]2[(nh,λ2κh,λ2)cosψ+nau]2+[2nh,λκh,λcosψ+nav]2
Display Formula
(5)eff,λ=,λ+,λ2
Display Formula
(6)2u2=(nh,λ2κh,λ2na2sin2ψ)+(nh,λ2κh,λ2na2sin2ψ)2+4nh,λ2κh,λ2
Display Formula
(7)2v2=(nh,λ2κh,λ2na2sin2ψ)+(nh,λ2κh,λ2na2sin2ψ)2+4nh,λ2κh,λ2

where na is the index of refraction of air u and v are the real and imaginary parts of a complex variable u+iv; ,λ, ,λ and eff,λ are spectral perpendicular and parallel and effective interface reflectance; and ψ is the angle of incidence. In the present work, for simplicity, the spectral reflectance has been assumed to independent of the incident angle (i.e., ψ=0). Moreover, the validity of the aforementioned assumption has also been verified in Angular Dependence of the Heat Mirror Optical Signatures.

Figure 3(a) shows the calculated spectral reflectance of the Sn-In2O3 coated glass. Furthermore, it has been compared with the experimental reflectance data (available for the same coating) as reported by Fan et al. [24] and Fan and Bachner [25] in the wavelength range from 0.3 μm to 10 μm. It reveals that the Drude free carrier model could accurately predict the spectral reflectance of Sn-In2O3 coated glass.

Figure 3(b) shows the calculated effective emittance (εh,eff) across the infrared region for various absorber temperatures calculated using the following equation [25]: Display Formula

(8)εh,eff=0.3μm100μm(1eff,λ)eb,T,λdλ0.3μm100μmeb,T,λdλ0.3μm100μm(1eff,λ)eb,T,λdλ0.3μm100μmeb,T,λdλ

where λ is the spectral effective reflectance (spectral normal reflectance in the present case), eb,T,λ is the spectral black body emissive power. Numeric integration has been carried out by inputting the calculated spectral data (λ,eb,T,λ) into the aforementioned equation with dλ=5nm.

Figure 3(a) reveals that the Sn-In2O3 coated glass has low effective thermal emittance even at high temperatures. Furthermore, the solar weighted transmittance of the Sn-In2O3 coated glass has been found to be ∼0.85 [26]. Thus, coating the glass with Sn-In2O3 could actually result in lower thermal losses without significantly impacting the optical efficiency of the system. Table 2 provides a comparison of the optical properties of the conventional (SEGS LS2) and the proposed receiver designs.

Optical Energy Balance.

First, solar irradiance flux distribution around the receiver tube is essentially nonuniform (see Fig. 4(a)). Second, coated and the uncoated portions of the glass envelope have different optical properties. Finally, the amount of flux reaching the selectively coated metal tube is also dependent on the angle (θ) up to which the glass envelope has been coated (see Fig. 4(b)). Therefore, in order to compute the optical efficiency of the parabolic trough collector, the three aforementioned factors should be considered in addition to the reflectance of the concentrator (ρ = 0.93) [17,18] and absorptivity of the selective coated metal tube.

Now, since the concentrated heat flux distribution is nonuniform around the receiver tube, its value is bound to be a function of the heat mirror angle. The concentrated heat flux for various regions can then be calculated using Eqs. (9)(12). Note that the following equations are valid for a rim angle of 70 deg.

For θ180Display Formula

(9)z=ρ[(θ360)τhS+(30360)τgg1+(70360)τgg2+(80360)τgg3+((180θ)360)τgS]

For 180<θ260Display Formula

(10)z=ρ[(180360)τhS+(30360)τgg1+(70360)τgg2+((θ180)360)τhg3+((260θ)360)τgg3]

For 260<θ330Display Formula

(11)z=ρ[(180360)τhS+(30360)τgg1+(80360)τhg3+((θ260)360)τhg2+((330θ)360)τgg2]

For 330<θ360Display Formula

(12)z=ρ[(180360)τhS+(70360)τhg2+(80360)τhg3+((θ330)360)τhg1+((360θ)360)τgg1]

where θ is the angle of coating on the glass envelope, τh is the transmittance of the coated portion of the glass envelope, and τg is the transmittance of the glass envelope, which is uncoated, g1 is the average concentrated heat flux for first region (330deg<θ<360deg) (Fig. 4(a)), g2 is the average concentrated heat flux for second region (260deg<θ<330deg) (Fig. 4(a)), g3 is the average concentrated heat flux for third region (180deg<θ<260deg) (Fig. 4(a)), ρ is the reflectance of the parabolic concentrator, S is the incident solar irradiation on the aperture, z is the concentrated solar irradiation. It may be noted that the values of g1,g2,g3 have been calculated using the flux distribution data from Ref. [28]. Now that we have got the spatial concentrated flux distribution around the receiver, the total concentrated heat flux on the receiver could be evaluated using the below equation: Display Formula

(13)z¯=zαm

where z¯ is the effective concentrated heat flux on the receiver tube to be useable, αm is the absorptivity of selectively coated metal receiver tube

Hence, the optical efficiency defined by Eq. (14) could be found as a function of θDisplay Formula

(14)ηop=z¯AroSAaperture

Figure 5 shows optical efficiency plotted as a function of heat mirror circumferential angle.

It is clearly apparent from Fig. 5 that there is a critical heat mirror circumferential angle (θ = 180 deg in the present study) above which the optical efficiency sharply decreases. Hence, θ should be carefully chosen to realize benefits of heat mirror in improving collector efficiency. A large value of θ may help in reducing the thermal loss area, but at the same time, large θ means sacrificing some optical efficiency (for instance in case θ > 180 deg).

Overall Energy Balance.

Once the amount of solar irradiance flux that is able to reach the selectively coated metal tube is known, the next step is to compute the overall energy balance. Quantification of the heat transfer mechanisms necessitates some reasonable assumptions to be made. These assumptions have been carefully made so that the model remains sufficiently accurate for engineering purposes and captures the physics behind each of the heat transfer processes.

  • (a)Spectrally distributed solar irradiance has been assumed to incident normally to the aperture.
  • (b)Uncoated portion of the glass envelope has solar weighted transmittance of 0.95.
  • (c)Coated portion of the glass envelope has solar weighted transmittance of 0.85.
  • (d)For the coated glass envelope portion, the infrared emission from the absorber tube is assumed to be eventually absorbed by the absorber tube (facing the coated portion of the glass envelope) and the coated portion depending on their emittance.
  • (e)For the uncoated glass envelope portion, the infrared emission from the absorber tube is assumed to be eventually absorbed by the absorber tube (facing the uncoated portion of the glass envelope) and the uncoated portion depending on their emittance.
  • (f)Although the baffles themselves take part in the radiative heat transfer process, for simplicity, this aspect has been neglected as surface area of the baffles is considerably smaller than the absorber and the envelope. In other words, the baffles ensure that there is no infiltration of the IR radiations between the coated and uncoated portions of the glass envelope, without taking part in the radiative heat transfer process. The detailed analysis that takes care of the reflection/absorption at the baffles has been described in Effect of Introducing Baffles on the Overall Radiative Heat Transfer Process. It reveals that the aforementioned simplifying assumption is indeed sufficiently accurate for modeling the radiative heat transfer process.
  • (g)For the absorber tube, the emittance has been assumed independent of the absorber tube temperature.
  • (h)Effective sky temperature has been assumed to be 8 deg less than the ambient temperature [27].
  • (i)As in the present model, the trough length is less than 100 m; therefore, one-dimensional steady-state heat transfer model gives satisfactory results [20,29]. Although the receiver's cross section is much smaller than its length, the rate of temperature rise is significantly high in the radial direction as compared to axial direction. Furthermore, the rate of thermal energy gain as the working fluid moves along the length is linear and constant for receiver lengths less than 100 m. As the length of the receiver increases (to about 1000 m), the temperature gradient along the axial direction (along the receiver length) tends to become nonlinear owing to significant change in the mass flow rate (due to change in the thermophysical properties, particularly mass density) and pressure drop along the length of the receiver [30]. Thus, receiver lengths exceedingly greater than 100 m necessitate two-dimensional steady-state models to capture the aforesaid nonlinearity and for receiver lengths less than 100 m one-dimensional steady-state model is sufficiently accurate.
  • (j)Under steady-state conditions, the amount of heat transferred from absorber tube to glass inner surface, then by conduction to outer surface, and then by outer surface to atmosphere is same.
  • (k)In actual practice, the temperature distribution across the circumference of the receiver is nonuniform and is similar to the incident flux distribution [31,32]. However, the overall performance characteristics such as thermal efficiency and thermal losses have been found to be negligibly effected whether nonuniform or uniform temperature thermal models are employed [33]. In the backdrop of the aforementioned fact and for simplicity, absorber tube and glass envelope temperatures have been assumed to be uniform across the circumference in the present work. Furthermore, the validity of this assumption in context of the proposed receiver design has also been verified in Effect of Absorber Tube Circumferential Temperature Distribution.

Heat transfer mechanisms involved: Fig. 6 details the various heat transfer mechanisms involved in the proposed receiver design. In Fig. 6; A, B, C, D, E, F, G, and H are as follows (defined in Table 3).

Energy balance equations were invoked for each component of the receiver. In terms of losses, first, the heat transfer from the absorber tube to the inner surface of the glass envelope has been analyzed. It essentially takes place by radiative heat transfer (since in the annulus vacuum is present, heat transfer through convection and conduction is negligibly small [20]) (see Eq. (15) and Fig. 6(a)). Next, the heat reaching the inner surface of the glass envelope is conducted to its outer surface (see Eq. (16) and Fig. 6(a)). Finally, the outer surface of the glass envelope rejects heat to the atmosphere through convection and radiation heat transfer (see Eq. (17) and Fig. 6(a)) Display Formula

(15)Qloss1=πDroLσ(Tro4Tgi4)1εr+1εgεg(360θθ)+πDroLσ(Tro4Tgi4)1εr+1εh,effεh,eff(θ360)
Display Formula
(16)Qloss2=2πkgL(TgiTgo)ln(DgoDgi)
Display Formula
(17)Qloss3=πDgoLhw(TgoTa)+εgπDgoLσ(Tgo4Tsky4)

Under steady-state conditions, Eq. (18) below applies (also apparent from Fig. 6(a)): Display Formula

(18)Qloss1=Qloss2=Qloss3=Qloss

Now, in order to evaluate Eq. (17), convective heat transfer coefficient between the envelope outer surface and the ambient air (wind conditions) needs to be calculated. In the present work, the empirical correlation as given in Ref. [20] has been employed (see Eq. (19)). Here, Pra and Prgo are the Prandtl numbers evaluated at the average ambient air and average glass cover outer surface temperatures, respectively. The values of C, n, and m could be found depending on the range of Prandtl and Reynolds number as detailed in Ref. [20] Display Formula

(19)Nua=CReamPran(PraPrgo)14

Subsequently, the convective heat transfer coefficient could be found as Display Formula

(20)ha=NuakaD4

Furthermore, in order to evaluate the convective heat transfer coefficients between the HTF and the absorber tube, Nusselt number empirical correlation for turbulent and transitional flow regimes [20,27] (given by Eq. (21)) has been used in the present work. Here, fr is the friction factor (given by Eq. (22)) of the inner surface of the absorber tube, Prf and Prf are the Prandtl numbers evaluated at the average HTF (Therminol VP-1 in the present work) and absorber tube temperatures, respectively, Display Formula

(21)Nuf=fr8(Ref1000)Pr11+12.7fr8(Prf231)(PrfPrr)0.11
Display Formula
(22)f2=(1.82log10(Ref)1.64)2

Once Nusselt number is known, we can calculate the corresponding heat transfer coefficient as Display Formula

(23)hf=NufkfD1

A code has been written in matlab to solve the aforementioned governing energy balance equations. Subsequent paragraphs describe the algorithm, which has been essentially implemented to calculate the performance parameters (such as thermal efficiency of the system) through solution of energy balance equations.

For a known steady-state absorber tube temperature (Tr), the resulting temperatures of the glass envelope (TgoandTgi) and the heat loss (Qloss) have been found by solving the aforementioned equations (Eqs. (15)(18)) using an iterative process.

First, Eq. (17) was solved for Qloss3 by assuming some outer glass envelope temperature (Tgo). The calculated loss occurring from envelop to atmosphere (Qloss3) was then equated in Eq. (16) to find inner glass envelope temperature (Tgi). Next, the calculated inner glass envelope temperature was used in Eq. (15) to find the resulting heat loss term (Qloss1). Finally, the calculated loss terms Qloss1 and Qloss3 were compared. If the difference was negligible, then the assumed/calculated temperatures (Tgi,Tgo) and the resulting loss term were in well agreement and the corresponding energy balance equations were satisfied. In case a significant difference between calculated loss terms Qloss1 and Qloss3 was observed, then the whole process was carried out for a new value of inner glass envelop temperature (Tgi). The iterative process was carried until the difference between calculated loss terms Qloss1 and Qloss3 became insignificant.

Now, with the help of the calculated heat loss term, the overall heat loss coefficient UL was evaluated (see Eq. (24)). Next, the collector efficiency factor F was calculated (see Eq. (25)). With the help of collector efficiency factor, collector flow factor F and the collector heat removal factor Fr were evaluated (see Eqs. (26) and (27)). Fr reflects the thermal energy gain by the working fluid as in transverses through the receiver length Display Formula

(24)UL=QlossAro(TrTa)
Display Formula
(25)F=1UL1UL+DrohfDri+Dro2kln(DroDri)
Display Formula
(26)F=mcpAroULF[1exp(AroULFmcp)]
Display Formula
(27)Fr=FF

Now, since we know the overall heat loss coefficient, the collector heat removal factor, and effective concentrated heat flux on the receiver, useful heat gain could be calculated using Eq. (28) as Display Formula

(28)Qusefull=(FrAroz¯FrAroUL(TrTa))

Finally, thermal efficiency of the PTC system has been evaluated using Eq. (29)Display Formula

(29)η=QusefullSAaperture

Solution of the optical and the overall energy balance equations gets us the values of the performance parameters such as optical and thermal losses (convection and radiation losses), useful heat gain, and thermal efficiency. In order to truly capture the performance of such novel collectors (employing hybrid glass envelope), it is imperative to study the effect of design (such as heat mirror circumferential angle) and operating parameters (such as absorber temperature, HTF flow rate, and wind speed), on the aforesaid performance parameters.

First, for different values of heat mirror circumferential angles (θ), glass envelope temperature has been evaluated as a function of selectively coated absorber tube temperature (see Fig. 7(a)). It is apparent from the plots that envelope temperature increases nonlinearly with increase in absorber temperature. This can be understood from the fact that heat transfer mechanism from the absorber tube to the glass envelope is predominantly radiation; therefore, with linear increase in absorber tube temperature, the heat transfer from the absorber tube to the glass envelope varies as Tr4.

Now, as the convection and radiation losses finally take place from the glass envelope to the surrounding/sky, these also increase nonlinearly with absorber tube temperature (see Figs. 7(b)7(d)). As far as the effect of circumferential heat mirror angle is concerned, it can be seen that with increase in θ, the envelope temperature and hence the thermal losses decrease.

However, the thermal efficiency does not follow the same trend (see Fig. 8), i.e., thermal efficiency is not always highest for the case of maximum circumferential angle (θ = 360 deg).

Next, the effect of wind speed is considered for various values of heat mirror angles. It can be seen from Fig. 9(a) that radiative losses decrease with increase in wind speed. This could be understood from the fact that under steady-state conditions, high wind speed means lesser outer glass cover temperature and hence lesser radiative losses. As for as convection heat losses are concerned, they follow the expected trend, i.e., they increase with wind speed (see Fig. 9(b)) owing to increase in the value of the convective heat transfer coefficient. Overall, the thermal losses do not vary much with wind speed owing to the aforementioned opposing convection and radiation losses trends.

Subsequently, the circumferential heat mirror angle is varied and its effect on the performance of the system is analyzed for different absorber tube temperatures. Figures 10(a) and 10(b) clearly show that for a given θ, losses are highest for the highest absorber tube temperature. Furthermore, the effect of absorber tube temperature diminishes as θ is increased from 0 deg to 360 deg (temperature isotherms tend to converge with increase in θ). This can be understood from the fact that at high θ values, essentially the thermal energy radiated by the absorber tube to the inner cover of the glass envelope is reflected back to the absorber tube; hence, the increased absorber tube temperature does not correspondingly result in increased thermal losses.

Figure 10(c) deciphers a very interesting characteristic of such novel solar thermal systems. Clearly, thermal efficiency increase with increase in θ only up to a certain value of θ, a value higher than this critical value tends to decrease the thermal efficiency. Although, thermal losses are always decreasing with increase in θ, but due to anomalous nature (see Fig. 5) of optical efficiency, the efficiency does not always increase with increase in θ; instead, it dips down in accordance with the optical efficiency of the system. When θ is increased from a value 0 deg to a value ≤180 deg, the decrease in thermal losses area dominates over the increase in the optical losses but as we increase θ beyond 180 deg, drastic increase in optical losses occurs, which dominates over the decrease in thermal loss area and hence the thermal efficiency of the system tends to decrease. Therefore, the system has the highest efficiency at 180 deg circumferential heat mirror angle.

Finally, the performance of the fourth generation state of the art SCHOTT PTR®70 coated absorber tube, when it is employed as the absorber tube in conventional and the proposed receiver designs has been evaluated (see Fig. 11). This particular coating has been chosen for comparison, as it serves as the benchmark for the parabolic trough receivers [9,10,34]. Figure 11 reveals that the two receiver designs have similar performance characteristics at low absorber tube temperatures. However, the proposed receiver design could further improve the performance of the parabolic trough (particularly at high absorber tube temperatures) relative to the conventional receiver design.

This section essentially intends to verify the correctness of the underlying assumptions of the formulation relevant to the proposed receiver design. Furthermore, performance parameters at limiting values of key operating parameters have been assessed to predict the utility of the proposed received design relative to the conventional receiver design.

Angular Dependence of the Heat Mirror Optical Signatures.

The results in Results and Discussion are based on the assumption that there is no angular dependence on optical characteristics of heat mirror (i.e., spectral normal reflectance in Fig. 3(a) has been employed for the evaluation of performance parameters). However, in reality, the emission from the absorber tube takes place in all possible directions, i.e., the infrared radiations from the absorber tube could be incident at the coated portion of the glass envelope at any angle of incidence. Therefore, it is imperative to assess, if the effective reflectance and hence the effective emittance of Sn-In2O3 coated glass is sensitive to angle of incidence.

In order to accomplish the aforementioned task, Eqs. (1)(7) have been employed and the angle of incidence (ψ) has been varied from 0 deg to 80 deg. Figure 12 clearly shows the angle of incidence does not have significant impact on the effective emittance of the heat mirror. Furthermore, the sensitivity of the emittance to the incident angle is noticeable only for ψ>60deg. This observation is consistent with that documented in the literature [35].

Effect of Absorber Tube Circumferential Temperature Distribution.

In the present work, the absorber tube temperature has been assumed to be uniform across the circumference. However, in actual practice, there is a temperature distribution around the absorber tube circumference. In order to quantitatively assess the correctness of the assumption in relation to the proposed receiver design, the entire receiver has been assumed to have two distinct temperature zones. These could be approximated to be two equal zones, with each zone characterized by a unique temperature. The first zone (zone 1) forms the lower half of the receiver (which receives the concentrated solar flux) and the second zone (zone 2) is the upper half of the receiver (which essentially receives 1 sun flux). The typical average temperature of zone 1 has been found to be ∼17% higher than that of zone 2 [3133]. In the present work (for θ = 180 deg), the zone 1 and zone to coincide with the uncoated and coated portions of the proposed receiver design. Now, in order to quantitatively include this in the theoretical model, Eq. (15) has been modified as Display Formula

(30)Qloss1=πDroLσ(Tro,uc4Tgi4)1εr+1εgεg(360θθ)+πDroLσ(Tro,c4Tgi4)1εr+1εh,effεh,eff(θ360)

It is similar to Eq. (15), except that the in the first and second terms on right side of Eq. (15), Tro (temperature of the absorber tube) has been replaced with Tro,uc (temperature of the absorber tube facing the uncoated envelope) and Tro,c (temperature of the absorber tube facing the coated envelope), respectively. Furthermore, the two temperatures are linked through the following relationships: Display Formula

(31)Tro,ucTro,c=1.17
Display Formula
(32)Tro=Tro,uc+Tro,c2

Now, Eqs. (16)(32) have been employed to calculate the thermal efficiency of the proposed receiver design.

Figure 13 reveals that it is indeed sufficiently accurate to assume uniform circumferential temperature distribution in case of absorber tube.

Combined Effects of Absorber Tube and Heat Mirror Effective Emittance on the Overall Performance.

In the proposed receiver design, the overall performance of the receiver depends on the relative magnitudes of the emittance of the absorber as well as the heat mirror.

First, let us vary the emittance of the absorber tube, keeping the effective emittance of the heat mirror fixed. Figure 14(a) reveals that for lower values of absorber tube emittance the thermal efficiency first increases and then decreases with increase in circumferential heat mirror angle (depicting that their exists an optimum value of θoptimum = 180 deg). However, for larger values of absorber tube emittance, the optimum heat mirror angle shifts to 360 deg. This may be attributed to the fact that at high absorber emittance, it is imperative to coat the complete envelope to ensure high thermal efficiency.

Finally, keeping the emittance of the absorber tube fixed, the effect of heat mirror emittance on the performance is assessed.

Here, for low heat mirror emittance, the value of θoptimum = 270 deg. Furthermore, for higher values of heat mirror emittance, the optimum heat mirror angle shifts to 180 deg (see Fig. 14(b)).

Effect of Introducing Baffles on the Overall Radiative Heat Transfer Process.

The results obtained in Results and Discussion were based on the simplifying assumptions that baffles do not allow the infiltration of the IR radiations between the coated and uncoated portions of the glass envelope (without taking part in the heat transfer process). However, the analysis overlooked the fact that the baffles shall themselves reflect as well absorb the incident IR radiations. Furthermore, the extent of reflectance and absorbance shall also be influenced by the relative orientation (view factor) of the optical elements (coated, uncoated portions of the glass envelope, absorber circumference, and the baffles) relative to each other.

Therefore, in order to quantify the radiative heat transfer among the various optical elements, it is imperative to calculate the relevant view factors. In the present study, the view factors have been found through Hottel's crossed string method given by the following equation: Display Formula

(33)Fij=(Crossedstrings)(Uncrossedstrings)2(Stringonsurfacei)

Figure 15 shows the schematic of a generic typical configuration.

Invoking the Hottel's crossed string method and identifying the relevant strings, we get Display Formula

(34)F12=(stringabc+stringebd)(stringda+stringce)2(Stringabe)

The relevant string lengths have been calculated and are represented by the following equation: Display Formula

(35)F12=Rgi2Rr2+(θcos1(RrRgi))Rr(RgiRr)θRr

Now, as we know quantitatively at least of the view factors, we could evaluate the rest of the view factors using the view factor algebra (see Eqs. (36)(42)). Note that as representative case θ has been taken to equal π radians, i.e., half of the glass envelope circumference is coated Display Formula

(36)F11=F33=0,convexsurfaces
Display Formula
(37)F11+F12+F13=1,summationrule
Display Formula
(38)F21+F22+F23=1,summationrule
Display Formula
(39)F31+F32+F33=1,summationrule
Display Formula
(40)A1F12=A2F21F21=RrRgiF12,reciprocityrule
Display Formula
(41)A3F31=A1F13F31=θRr2(RgiRr)F13,reciprocityrule
Display Formula
(42)A2F23=A3F32F23=2(RgiRr)θRgiF32,reciprocityrule

Now that we know the numeric values of the view factors, next step is to compute the net radiative heat transfer from each of the surfaces involved through the following set of equations: Display Formula

(43)Q1A1=(ε11ε1)(σT14J1)=J1(J1F11+J2F12+J3F13)Q2A2=(ε21ε2)(σT24J2)=J2(J1F21+J2F22+J3F23)Q3A3=(ε31ε3)(σT34J3)=J3(J1F31+J2F32+J3F33)

The above set of equations could be rearranged in the following form so that there are three equations in three unknowns, which could then be simultaneously solved to get J1, J2, and J3: Display Formula

(44)(1F11+ε11ε1)J1F12J2F13J3=ε11ε1σT14F21J1+(1F22+ε21ε2)J2F23J3=ε21ε2σT24F31J1F32J2+(1F33+ε31ε3)J3=ε31ε3σT34

Table 4 details the emittance values employed in the present study.

Finally, the J values could be employed to calculate the net radiative heat transfer from surfaces. Hence, the heat loss from the absorber tube to the glass envelope now takes the following form: Display Formula

(45)Qloss1=Q2,coated+Q2,uncoated

Figure 16 depicts the thermal efficiency as a function of absorber tube temperature when the baffles are included in the radiative heat transfer process. Namely two extreme cases have been explored. Case 1: the baffle is assumed to be at absorber tube temperature (worst case scenario), and case 2: the baffle is assumed to be at inside glass envelope temperature (best case scenario). Furthermore, curves for conventional receiver design as well as for the case when effect of baffles is neglected have also been included in the figure.

It is clear from the plots that even in the worst case scenario, i.e., when the baffles reach the absorber temperature, the proposed configuration outperforms the conventional receiver design.

In the present study, a novel parabolic trough receiver design has been proposed. It has been found that through usage of hybrid glass envelope (having coated and uncoated portions), it is possible (under certain controlled conditions) to engineer a parabolic receiver design that has 3–5% higher thermal efficiency as compared to its surface absorption based counterpart. The uncoated portion ensures high transmittance in the solar irradiance wavelength band and the coated portion ensures high reflectance in the midinfrared region. The aforementioned characteristics lend it to reduce thermal loss area without compromising with the optical efficiency of the system.

For a given rim angle of the parabolic trough, there exists a critical value of circumferential heat mirror angle (θ), which denotes the maximum angle up to which the envelope should be coated with Sn-In2O3. Heat mirror angles exceeding this critical value instead decrease the optical and hence thermal efficiency of the system.

Furthermore, it may be noted that in addition to the efficiency improvements, the usage of hybrid glass envelope could actually prove to be a significant step in relaxing the requirement of high temperature-resistant selective coatings. This is envisaged, as in the proposed receiver design and its variants (opposed to the conventional receiver design), the objectives of high absorptivity and low emissivity could be fulfilled by two different components. In other words, receiver designs having a nonselective absorber tube and the hybrid envelope could actually be realized, which is expected to have performance characteristics comparable to the conventional receiver designs.

It may be noted that the proposed receiver design modification is expected to add to the capital as well as maintenance costs. Therefore, more research addressing the cost and retrofitting issues is required to realize and ensure suitability of the proposed receiver design in the existing parabolic trough collectors.

V.K., P.M., and M.M. acknowledge the support provided by the Mechanical Engineering Department at Thapar University Patiala.

  • Aaperture =

    aperture area (m2)

  • Ar =

    receiver area (m2)

  • cp =

    specific heat (Jkg−1 K−1)

  • Dgi =

    inner diameter of glass envelope (0.105 m)

  • Dgo =

    outer diameter of glass envelope (0.115 m)

  • Dri =

    inner diameter of selective metal absorber tube (0.064 m)

  • Dro =

    outer diameter of selective metal absorber tube (0.07 m)

  • E =

    photon energy (eV)

  • Ec =

    relaxation energy (0.075 eV)

  • Ep =

    plasma energy (1.64 eV)

  • F′ =

    collector efficiency factor

  • F″ =

    collector flow factor

  • Fij =

    view factor

  • Fr =

    collector heat removal factor

  • g1, g2, g3 =

    average concentrated heat flux for first, second and third regions, respectively, in (Wm−2), g1 = 3.3327 × 104, g2 = 4.2157 × 104, g3 = 2.4411 × 104

  • Fij =

    view factor

  • Fij =

    view factor

  • hf =

    convective heat transfer coefficient for fluid flow in receiver tube (166.3 Wm−2 K−1)

  • hw =

    convective heat transfer coefficient between glass envelope and surrounding (10.8 Wm−2 K−1)

  • J =

    radiosity (Wm−2)

  • kg =

    thermal conductivity of glass envelope (1.4 Wm−1 K−4)

  • kr =

    thermal conductivity of receiver tube (16 Wm−1 K−1)

  • L =

    length of aperture (7.8 m)

  • m ′ =

    mass flow rate of the HTF (0.9997 kgs−1)

  • na =

    index of refraction of air (=1)

  • nh,λ =

    spectral index of refraction of heat mirror

  • Qloss =

    thermal loss (W)

  • Qusefull =

    useful thermal energy (W)

  • S =

    solar irradiance (807 Wm−2)

  • Ta =

    air temperature (288.8 K)

  • Tbf =

    baffle temperature (K)

  • Tgi =

    glass inner surface temperature (K)

  • Tgo =

    glass outer surface temperature (K)

  • Tr =

    receiver temperature (K)

  • Tsky =

    sky temperature (K)

  • UL =

    loss coefficient

  • W =

    width of aperture (5 m)

  • z =

    concentrated heat flux on the receiver tube (Wm−2)

  • z¯ =

    effective concentrated heat flux on the receiver tube (Wm−2)

 Greek Symbols
  • αm =

    absorptivity of selectively coated metal receiver tube in the solar irradiation wavelength band

  • εg =

    emittance of glass envelope (uncoated portion)

  • εh,eff =

    emittance of glass envelope (coated portion)

  • εr =

    emittance of metal absorber tube

  • ε =

    adjustment parameter (=4.45)

  • ηth =

    thermal efficiency of the system (%)

  • θ =

    heat mirror circumferential angle (deg)

  • θoptimum =

    optimum value of heat mirror angle (deg)

  • κh,λ =

    spectral index of absorption of heat mirror

  • ρ =

    reflectance of the aperture trough

  • σ =

    Stephen–Boltzmann constant (Wm K−4)

  • τg =

    transmittance of the glass envelope (uncoated portion)

  • τh =

    transmittance of the glass envelope (coated portion)

  • ψ =

    angle of incidence (deg)

 Abbreviations
  • HTF =

    heat transfer fluid

  • LCR =

    local concentration ratio

Hafeza, A. Z. , Attia, A. M. , Eltwab, H. S. , ElKousy, A. O. , Afifi, A. A. , AbdElhamid, A. G. , AbdElqader, A. N. , Fateen, S.-E. K. , El-Metwallya, K. A. , Solimana, A. , and Ismail, I. M. , 2018, “Design Analysis of Solar Parabolic Trough Thermal Collectors,” Renewable Sustainable Energy Rev., 82, pp. 1215–1260. [CrossRef]
Kumaresan, G. , Sudhakar, P. , Santosh, R. , and Velraj, R. , 2017, “Experimental and Numerical Studies of Thermal Performance Enhancement in the Receiver Part of Solar Parabolic Trough Collectors,” Renewable Sustainable Energy Rev., 77, pp. 1363–1374. [CrossRef]
Price, H. , Lüpfert, E. , Kearney, D. , Zarza, E. , Cohen, G. , Gee, R. , and Mahoney, R. , 2002, “Advances in Parabolic Trough Solar Power Technology,” ASME J. Sol. Energy Eng., 124(2), pp. 109–125. [CrossRef]
May Tzuc, O. , Bassam, A. , Escalante Soberanis, M. A. , Venegas-Reyes, E. , Jaramillo, O. A. , Ricalde, L. J. , Ordonez, E. E. , and El Hamzaoui, Y. , 2017, “Modeling and Optimization of a Solar Parabolic Trough Concentrator System Using Inverse Artificial Neural Network,” J. Renewable Sustainable Energy, 9(1), p. 013701. [CrossRef]
Liu, Z. , Hao, L. , Liu, K. , Yu, H. , and Cheng, K. , 2017, “Design of High-Performance Water-in-Glass Evacuated Tube Solar Water by a High-Throughput Screening Based on Machine Learning: A Combined Modeling and Experimental Study,” Sol. Energy, 142, pp. 61–67. [CrossRef]
Hao, L. , Liu, Z. , Liu, K. , and Zhang, Z. , 2017, “Predictive Power of Machine Learning for Optimizing Solar Water Heater Performance: The Potential Application of High-Throughput Screening,” Int. J. Photoenergy, 2017, pp. 1–10.
Khullar, V. , Bhalla, V. , and Tyagi, H. , 2017, “Potential Heat Transfer Fluids (Nanofluids) for Direct Volumetric Absorption-Based Solar Thermal Systems,” ASME J. Therm. Sci. Eng. Appl., 10(1), p. 011009. [CrossRef]
Khullar, V. , Tyagi, H. , Patrick, P. E. , Otanicar, T. P. , Singh, H. , and Taylor, R. A. , 2013, “Solar Energy Harvesting Using Nanofluids-Based Concentrating Solar Collector,” ASME J. Nanotechnol. Eng. Med., 3(3), p. 031003. [CrossRef]
Yang, H. , Wang, Q. , Huang, X. , Li, J. , and Pei, G. , 2018, “Performance Study and Comparative Analysis of Traditional and Double-Selective Coated Parabolic Trough Receivers,” Energy, 145, pp. 206–216. [CrossRef]
Wang, Q. , Li, J. , Yang, H. , Su, K. , and Pei, G. , 2017, “Performance Analysis on a High-Temperature Solar Evacuated Receiver With an Inner Radiation Shield,” Energy, 139, pp. 447–458. [CrossRef]
Fuqiang, W. , Jianyu, T. , Lanxin, M. , and Chengchao, W. , 2015, “Effects of Glass Cover on Heat Flux Distribution for Tube Receiver With Parabolic Trough Collector System,” Energy Convers. Manage., 90, pp. 47–52. [CrossRef]
Daniel, P. , Joshi, Y. , and Das, A. K. , 2011, “Numerical Investigation of Parabolic Trough Receiver Performance With Outer Vacuum Shell,” Sol. Energy, 85(9), pp. 1910–1914. [CrossRef]
Al-Ansary, H. , and Zeitoun, O. , 2011, “Numerical Study of Conduction and Convection Heat Losses From a Half-Insulated Air-Filled Annulus of the Receiver of a Parabolic Trough Collector,” Sol. Energy, 85(11), pp. 3036–3045. [CrossRef]
Jeter, S. M. , 1987, “Analytical Determination of the Optical Performance of Practical Parabolic Trough Collectors From Design Data,” Sol. Energy, 39(1), pp. 11–21. [CrossRef]
Jeter, S. M. , 1986, “Calculation of the Concentrated Flux Density Distribution in Parabolic Trough Collectors by a Semifinite Formulation,” Sol. Energy, 37(5), pp. 335–345. [CrossRef]
Galindo, J. , and Bilgen, E. , 1984, “Flux and Temperature Distribution in the Receiver of Parabolic Solar Furnaces,” Sol. Energy, 33(2), pp. 125–135. [CrossRef]
Sadaghiyani, O. K. , Pesteei, S. M. , and Mirzaee, I. , 2014, “Numerical Study on Heat Transfer Enhancement and Friction Factor of LS-2 Parabolic Solar Collector,” ASME J. Therm. Sci. Eng. Appl., 6(1), p. 012001. [CrossRef]
Dudley, V. E. , Kolb, G. J. , Sloan, M. , and Kearney, D. , 1994, “Test Results, SEGS LS-2 Solar Collector,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND94-1884.
Timothy, M. A. , and Brosseau, D. A. , 2005, “Final Test Results for the Schott HCE on a LS-2 Collector,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2005-4034.
Forristall, R. , 2003, “Heat Transfer Analysis and Modelling of a Parabolic Trough Solar Receiver Implemented in Engineering Equation Solver,” National Renewable Energy Technology, Golden, CO, Report No. NREL/TP 550-34169. http://fac.ksu.edu.sa/sites/default/files/34169.pdf
Fan, J. C. , and Bachner, F. J. , 1975, “Properties of Sn-Doped In2O3 Films Prepared by RF Sputtering,” J. Electrochem. Soc., 122(12), pp. 1719–1725. [CrossRef]
Yoshida, S. , 1978, “Efficiency of Drude Mirror-Type Selective Transparent Filters for Solar Thermal Conversion,” Appl. Opt., 17(1), pp. 145–149. [CrossRef] [PubMed]
Brewster, M. Q. , 1992, Thermal Radiative Transfer and Properties, Wiley, New York.
Fan, J. C. C. , Bachner, F. J. , Foley, G. H. , and Zavracky, P. M. , 1974, “Transparent Heat Mirror Films of TiO2/Ag/TiO2 for Solar Energy Collection and Radiation Insulation,” Appl. Phys. Lett., 25(12), p. 693. [CrossRef]
Fan, J. C. , and Bachner, F. J. , 1976, “Transparent Heat Mirrors for Solar-Energy Applications,” Appl. Opt., 15(4), pp. 1012–1017. [CrossRef] [PubMed]
Khullar, V. , 2014, “Heat Transfer Analysis and Optical Characterization of Nanoparticle Dispersion Based Solar Thermal Systems,” Ph.D. thesis, Indian Institute of Technology Ropar, Rupnagar, Punjab, India.
Duffie, J. A. , and Beckman, W. A. , 2006, Solar Engineering of Thermal Processes, Wiley, Hoboken, NJ.
He, Y. L. , Xiao, J. , Cheng, Z. D. , and Tao, Y. B. , 2011, “A MCRT and FVM Coupled Simulation Method for Energy Conversion Process in Parabolic Trough Solar Collector,” Renewable Energy, 36(3), pp. 976–985. [CrossRef]
Liang, H. , You, S. , and Zhang, H. , 2015, “Comparison of Different Heat Transfer Models for Parabolic Trough Solar Collectors,” Appl. Energy, 148, pp. 105–114. [CrossRef]
Yilmaz, I. H. , and Soylemez, M. S. , 2014, “Thermo-Mathematical Modelling of Parabolic Trough Collector,” Energy Convers. Manage., 88, pp. 768–784. [CrossRef]
Patil, R. G. , Panse, S. V. , and Joshi, J. B. , 2014, “Optimization of Non-Evacuated Receiver of Solar Collector Having Non-Uniform Temperature Distribution for Minimum Heat Loss,” Energy Convers. Manage., 85, pp. 70–84. [CrossRef]
Wu, Z. , Li, S. , Yuan, G. , Lei, D. , and Wang, Z. , 2014, “Three-Dimensional Numerical Study of Heat Transfer Characteristics of Parabolic Trough Receiver,” Appl. Energy, 113, pp. 902–911. [CrossRef]
Cheng, Y. , He, Y. , and Qiu, Y. , 2015, “A Detailed Nonuniform Thermal Model of a Parabolic Trough Solar Receiver With Two Halves and Two Inactive Ends,” Renewable Energy, 74, pp. 139–147. [CrossRef]
SCHOTT Solar CSP GmbH, 2008, “SCHOTT PTR®70 Receiver,” SCHOTT Solar, Mainz, Germany, accessed Jan. 15, 2018, http://www.schott.com/d/csp/370a8801-3271-4b2a-a3e6-c0b5c78b01ae/1.0/schott_ptr70_4th_generation_brocure.pdf
Pracchia, J. A. , and Simon, J. M. , 1981, “Transparent Heat Mirrors: Influence of the Materials on the Optical Characteristics,” Appl. Opt., 20(2), pp. 251–258. [CrossRef] [PubMed]
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References

Hafeza, A. Z. , Attia, A. M. , Eltwab, H. S. , ElKousy, A. O. , Afifi, A. A. , AbdElhamid, A. G. , AbdElqader, A. N. , Fateen, S.-E. K. , El-Metwallya, K. A. , Solimana, A. , and Ismail, I. M. , 2018, “Design Analysis of Solar Parabolic Trough Thermal Collectors,” Renewable Sustainable Energy Rev., 82, pp. 1215–1260. [CrossRef]
Kumaresan, G. , Sudhakar, P. , Santosh, R. , and Velraj, R. , 2017, “Experimental and Numerical Studies of Thermal Performance Enhancement in the Receiver Part of Solar Parabolic Trough Collectors,” Renewable Sustainable Energy Rev., 77, pp. 1363–1374. [CrossRef]
Price, H. , Lüpfert, E. , Kearney, D. , Zarza, E. , Cohen, G. , Gee, R. , and Mahoney, R. , 2002, “Advances in Parabolic Trough Solar Power Technology,” ASME J. Sol. Energy Eng., 124(2), pp. 109–125. [CrossRef]
May Tzuc, O. , Bassam, A. , Escalante Soberanis, M. A. , Venegas-Reyes, E. , Jaramillo, O. A. , Ricalde, L. J. , Ordonez, E. E. , and El Hamzaoui, Y. , 2017, “Modeling and Optimization of a Solar Parabolic Trough Concentrator System Using Inverse Artificial Neural Network,” J. Renewable Sustainable Energy, 9(1), p. 013701. [CrossRef]
Liu, Z. , Hao, L. , Liu, K. , Yu, H. , and Cheng, K. , 2017, “Design of High-Performance Water-in-Glass Evacuated Tube Solar Water by a High-Throughput Screening Based on Machine Learning: A Combined Modeling and Experimental Study,” Sol. Energy, 142, pp. 61–67. [CrossRef]
Hao, L. , Liu, Z. , Liu, K. , and Zhang, Z. , 2017, “Predictive Power of Machine Learning for Optimizing Solar Water Heater Performance: The Potential Application of High-Throughput Screening,” Int. J. Photoenergy, 2017, pp. 1–10.
Khullar, V. , Bhalla, V. , and Tyagi, H. , 2017, “Potential Heat Transfer Fluids (Nanofluids) for Direct Volumetric Absorption-Based Solar Thermal Systems,” ASME J. Therm. Sci. Eng. Appl., 10(1), p. 011009. [CrossRef]
Khullar, V. , Tyagi, H. , Patrick, P. E. , Otanicar, T. P. , Singh, H. , and Taylor, R. A. , 2013, “Solar Energy Harvesting Using Nanofluids-Based Concentrating Solar Collector,” ASME J. Nanotechnol. Eng. Med., 3(3), p. 031003. [CrossRef]
Yang, H. , Wang, Q. , Huang, X. , Li, J. , and Pei, G. , 2018, “Performance Study and Comparative Analysis of Traditional and Double-Selective Coated Parabolic Trough Receivers,” Energy, 145, pp. 206–216. [CrossRef]
Wang, Q. , Li, J. , Yang, H. , Su, K. , and Pei, G. , 2017, “Performance Analysis on a High-Temperature Solar Evacuated Receiver With an Inner Radiation Shield,” Energy, 139, pp. 447–458. [CrossRef]
Fuqiang, W. , Jianyu, T. , Lanxin, M. , and Chengchao, W. , 2015, “Effects of Glass Cover on Heat Flux Distribution for Tube Receiver With Parabolic Trough Collector System,” Energy Convers. Manage., 90, pp. 47–52. [CrossRef]
Daniel, P. , Joshi, Y. , and Das, A. K. , 2011, “Numerical Investigation of Parabolic Trough Receiver Performance With Outer Vacuum Shell,” Sol. Energy, 85(9), pp. 1910–1914. [CrossRef]
Al-Ansary, H. , and Zeitoun, O. , 2011, “Numerical Study of Conduction and Convection Heat Losses From a Half-Insulated Air-Filled Annulus of the Receiver of a Parabolic Trough Collector,” Sol. Energy, 85(11), pp. 3036–3045. [CrossRef]
Jeter, S. M. , 1987, “Analytical Determination of the Optical Performance of Practical Parabolic Trough Collectors From Design Data,” Sol. Energy, 39(1), pp. 11–21. [CrossRef]
Jeter, S. M. , 1986, “Calculation of the Concentrated Flux Density Distribution in Parabolic Trough Collectors by a Semifinite Formulation,” Sol. Energy, 37(5), pp. 335–345. [CrossRef]
Galindo, J. , and Bilgen, E. , 1984, “Flux and Temperature Distribution in the Receiver of Parabolic Solar Furnaces,” Sol. Energy, 33(2), pp. 125–135. [CrossRef]
Sadaghiyani, O. K. , Pesteei, S. M. , and Mirzaee, I. , 2014, “Numerical Study on Heat Transfer Enhancement and Friction Factor of LS-2 Parabolic Solar Collector,” ASME J. Therm. Sci. Eng. Appl., 6(1), p. 012001. [CrossRef]
Dudley, V. E. , Kolb, G. J. , Sloan, M. , and Kearney, D. , 1994, “Test Results, SEGS LS-2 Solar Collector,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND94-1884.
Timothy, M. A. , and Brosseau, D. A. , 2005, “Final Test Results for the Schott HCE on a LS-2 Collector,” Sandia National Laboratories, Albuquerque, NM, Report No. SAND2005-4034.
Forristall, R. , 2003, “Heat Transfer Analysis and Modelling of a Parabolic Trough Solar Receiver Implemented in Engineering Equation Solver,” National Renewable Energy Technology, Golden, CO, Report No. NREL/TP 550-34169. http://fac.ksu.edu.sa/sites/default/files/34169.pdf
Fan, J. C. , and Bachner, F. J. , 1975, “Properties of Sn-Doped In2O3 Films Prepared by RF Sputtering,” J. Electrochem. Soc., 122(12), pp. 1719–1725. [CrossRef]
Yoshida, S. , 1978, “Efficiency of Drude Mirror-Type Selective Transparent Filters for Solar Thermal Conversion,” Appl. Opt., 17(1), pp. 145–149. [CrossRef] [PubMed]
Brewster, M. Q. , 1992, Thermal Radiative Transfer and Properties, Wiley, New York.
Fan, J. C. C. , Bachner, F. J. , Foley, G. H. , and Zavracky, P. M. , 1974, “Transparent Heat Mirror Films of TiO2/Ag/TiO2 for Solar Energy Collection and Radiation Insulation,” Appl. Phys. Lett., 25(12), p. 693. [CrossRef]
Fan, J. C. , and Bachner, F. J. , 1976, “Transparent Heat Mirrors for Solar-Energy Applications,” Appl. Opt., 15(4), pp. 1012–1017. [CrossRef] [PubMed]
Khullar, V. , 2014, “Heat Transfer Analysis and Optical Characterization of Nanoparticle Dispersion Based Solar Thermal Systems,” Ph.D. thesis, Indian Institute of Technology Ropar, Rupnagar, Punjab, India.
Duffie, J. A. , and Beckman, W. A. , 2006, Solar Engineering of Thermal Processes, Wiley, Hoboken, NJ.
He, Y. L. , Xiao, J. , Cheng, Z. D. , and Tao, Y. B. , 2011, “A MCRT and FVM Coupled Simulation Method for Energy Conversion Process in Parabolic Trough Solar Collector,” Renewable Energy, 36(3), pp. 976–985. [CrossRef]
Liang, H. , You, S. , and Zhang, H. , 2015, “Comparison of Different Heat Transfer Models for Parabolic Trough Solar Collectors,” Appl. Energy, 148, pp. 105–114. [CrossRef]
Yilmaz, I. H. , and Soylemez, M. S. , 2014, “Thermo-Mathematical Modelling of Parabolic Trough Collector,” Energy Convers. Manage., 88, pp. 768–784. [CrossRef]
Patil, R. G. , Panse, S. V. , and Joshi, J. B. , 2014, “Optimization of Non-Evacuated Receiver of Solar Collector Having Non-Uniform Temperature Distribution for Minimum Heat Loss,” Energy Convers. Manage., 85, pp. 70–84. [CrossRef]
Wu, Z. , Li, S. , Yuan, G. , Lei, D. , and Wang, Z. , 2014, “Three-Dimensional Numerical Study of Heat Transfer Characteristics of Parabolic Trough Receiver,” Appl. Energy, 113, pp. 902–911. [CrossRef]
Cheng, Y. , He, Y. , and Qiu, Y. , 2015, “A Detailed Nonuniform Thermal Model of a Parabolic Trough Solar Receiver With Two Halves and Two Inactive Ends,” Renewable Energy, 74, pp. 139–147. [CrossRef]
SCHOTT Solar CSP GmbH, 2008, “SCHOTT PTR®70 Receiver,” SCHOTT Solar, Mainz, Germany, accessed Jan. 15, 2018, http://www.schott.com/d/csp/370a8801-3271-4b2a-a3e6-c0b5c78b01ae/1.0/schott_ptr70_4th_generation_brocure.pdf
Pracchia, J. A. , and Simon, J. M. , 1981, “Transparent Heat Mirrors: Influence of the Materials on the Optical Characteristics,” Appl. Opt., 20(2), pp. 251–258. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Details of selected surface absorption based parabolic trough receiver designs in the literature

Grahic Jump Location
Fig. 2

Schematic showing (a) parabolic trough collector, (b) conventional receiver design, and (c) the proposed receiver design

Grahic Jump Location
Fig. 3

(a) Spectral normal reflectance and (b) Effective emittance as a function of absorber tube temperature of Sn-In2O3 coated glass envelope

Grahic Jump Location
Fig. 4

(a) Local concentration ratio around the receiver of a parabolic trough having rim angle 70 deg (data points taken from Ref. [28]), and (b) schematic showing the regions of the hybrid glass envelope having different optical properties; θ denotes the angle up to which the glass envelope has been coated

Grahic Jump Location
Fig. 5

Optical efficiency of parabolic trough as a function of heat mirror circumferential angle

Grahic Jump Location
Fig. 6

(a) Schematic showing the thermal resistance model and (b) the heat transfer mechanisms involved in proposed receiver design

Grahic Jump Location
Fig. 7

For different values of circumferential heat mirror angles (a) envelope temperature as function absorber tube temperature, (b) convection losses as function absorber tube temperature, (c) radiation losses as function absorber tube temperature, and (d) total thermal losses as function absorber tube temperature. Wind speed 1 ms−1 and DNI = 807 Wm−2.

Grahic Jump Location
Fig. 8

Thermal efficiency as a function of absorber tube temperature for different circumferential heat mirror angle. Wind speed 1 ms−1 and DNI = 807 Wm−2.

Grahic Jump Location
Fig. 9

For a given absorber tube temperature and for different values of θ (a) radiation losses as a function of wind speed, (b) convection losses as a function of wind speed, and (c) thermal losses as a function of wind speed

Grahic Jump Location
Fig. 10

For various absorber tube temperatures (a) radiation losses as a function of θ, (b) convection losses as a function of θ, and (c) thermal efficiency as a function of θ. Wind speed 1 ms−1 and DNI = 807 Wm−2.

Grahic Jump Location
Fig. 11

Thermal efficiency as a function of absorber tube temperature for the proposed and conventional receiver designs employing SCHOTT PTR®70 coated absorber tube

Grahic Jump Location
Fig. 12

Effect of incidence angle on the effective emittance of the heat mirror for various absorber tube temperatures. Wind speed 1 ms−1 and DNI = 807 Wm−2.

Grahic Jump Location
Fig. 13

Thermal efficiency as a function of absorber tube temperature for nonuniform and uniform absorber tube temperature

Grahic Jump Location
Fig. 14

(a) For a given heat mirror emittance, the effect of absorber tube emittance on the thermal efficiency of the receiver and (b) for a given absorber tube emittance, the effect of heat mirror emittance on the thermal efficiency of the receiver. Wind speed 1 ms−1, DNI = 807 Wm−2, and Tr = 600 °C.

Grahic Jump Location
Fig. 15

Schematic showing the application of Hottel's string method. Circular arc “abe” (portion of receiver circumference) represents surface 1, circular arc “dc” (coated or un-coated portion of the glass envelope as the case may be) represents the surface 2, and combined “ce” and “da” (baffles) represent the surface 3, respectively.

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Fig. 16

Effect of baffles on the thermal efficiency of the parabolic trough collector. Wind speed 1 ms−1 and DNI = 807 Wm−2.

Tables

Table Grahic Jump Location
Table 1 Geometrical properties of parabolic trough collector components [17,18,20]
Table Grahic Jump Location
Table 2 Optical properties of the conventional (SEGS LS2) and the proposed receiver designs
Table Footer NoteaAverage value over the infrared wavelength band (value taken from Ref. [27]).
Table Footer NotebAverage value over the solar irradiance wavelength band (value taken from Refs. [17] and [18]).
Table Footer NotecAverage value over solar irradiance wavelength band (value taken from Refs. [17] and [18]).
Table Footer NotedAverage value over the infrared wavelength band (value taken from Refs. [17] and [18]).
Table Footer NoteeAverage value (at 100 °C absorber tube temperature) over the infrared wavelength band, 1–100 μm. This value varies with the magnitude of the absorber tube temperature, as it dictates the spectral distribution of the emitted radiation from the absorber tube to the coated portion of the glass envelope (see Fig. 3(b)).
Table Footer NotefAveraged over solar irradiance wavelength band 0.2–2.5 μm (data points for calculation have been taken from Ref. [26]).
Table Grahic Jump Location
Table 3 Heat transfer mechanisms involved in the proposed receiver design
Table Grahic Jump Location
Table 4 Emittance values for various optical elements

Errata

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