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Progress in the design and the applications of Linear Fresnel Reflectors – A

critical review

Article · May 2019

DOI: 10.1016/j.tsep.2019.01.014

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 Progress in the design and the applications of Linear Fresnel
Reflectors – A critical review

Evangelos Bellos

(bellose@central.ntua.gr)

Thermal Department, School of Mechanical Engineering, National Technical

University of Athens, Greece

Abstract:

Solar concentrating power is one of the most promising ways of producing clean
electricity by utilizing the incident solar irradiation on the earth. Linear Fresnel
reflector (LFR) is one of the major concentrating solar systems for producing useful
heat in medium and high-temperature levels (< 500oC). The LFR is a low-cost
technology which presents sufficient thermal performance and so it is characterized as
an interesting and valuable choice for utilizing the solar irradiation. The objective of
this work is to summarize the existing designs of LFR and the novel ideas which aim
to enhance the LFR performance. These ideas regard the optical and the thermal
efficiency increase. Moreover, the LFR is compared with rival technology, the
parabolic trough solar collector. The thermal and power applications with the LFR are
also studied in this review paper. The final conclusions of this work indicate the
future trends for this solar system and summarize the existing situation.

Keywords:

Linear Fresnel Reflector, solar energy, concentrating solar power, optical analysis,
thermal analysis, alternative design

1
 Table of contents

1. Introduction
1.1 Solar energy and applications
1.2 Solar concentrating collectors
1.3 The present work
2. The linear Fresnel reflector – main characteristics
2.1 The convectional LFR design
2.2 Basic mathematical formulation of LFR
2.2.1 Geometrical analysis
2.2.2 Optical analysis
2.2.3 Thermal analysis
2.3 Existing CSP with LFR
2.4 Comparison with PTC
3. Design of LFR
3.1 Primary concentrator designs
3.2 Receiver designs
3.2.1 Evacuated tube receivers
3.2.2 Cavity receivers
3.2.3 Alternative receivers
4. Applications with LFR in LFR
4.1 Power production applications
4.2 Cogeneration systems
4.3 Refrigeration systems
4.4 Desalination systems
4.5 Other applications
5. Discussion
5.1 Discussion of the different primary reflector designs
5.2 Discussion of the different receiver designs
5.3 Discussion of the LFR applications
5.4 Future trends
6. Conclusions

2
1. Introduction
1.1 Solar energy and applications
Solar energy exploitation is an important weapon for facing crucial dangers such the
global warming [1], the fossil fuel depletion [2], the increased energy demand due to
the new lifestyle trends [3] and the high electricity price [4]. The solar irradiation
which reaches on the earth is able to cover all the human needs. More specifically, if
it was possible to utilize all the incident solar irradiation on the earth for about one
hour and a half, then the yearly energy needs of the human beings could be totally
covered [5]. So, it can be said that solar energy is an abundant energy source [6]
which can be either converted to useful heat [7] or directly to electricity [8]. Solar
thermal collectors are the devices which can convert the incident solar irradiation into
useful heat, while photovoltaic panels convert it directly to electricity. The hybrid
collectors or thermal photovoltaic produce both heating and electricity. Usually, a
concentrator is applied into to the solar systems in order to concentrate the solar
irradiation into the absorbing surface and to generate higher temperature levels, the
fact that makes possible the application of solar collectors and especially the thermal
collectors in numerous applications. The most usual applications are for power
generation [9], heating production [10], cooling production [11], desalination [12],
industrial heat [13] and chemical processes [14].

1.2 Solar concentrating collectors

Concentrating solar thermal collectors are the devices which use a concentrator in
order to concentrate the incident direct beam irradiation in the absorber area. So, high-
temperature levels can be achieved because the heat flux values are high and so the
thermal losses are restricted due to the small absorbing area. Solar concentrating
technologies are separated into linear and point focus technologies. The linear
technologies are the parabolic trough collector (PTC) and the Linear Fresnel reflector
(LFR) [15], while the point focal are the solar dish concentrators and the solar towers
(or central systems) [16].

The most usual solar concentrating systems are the linear because the majority of the
worldwide projects are based on them [17]. The linear concentrating systems consist
of a linear concentrator and a linear absorber. The concentrator has a parabolic shape
or a segmented parabolic shape, while the absorber is located to the focal line (or very
close to it). PTC is the most mature solar concentrating technology, while LFR is an
evolving technology which is not well-established yet [17]. These are competitive
technologies which can be applied for applications up to 500 oC with thermal oil,
water/steam and molten salts as the working fluids [18]. The advantage of the PTC is
the high efficiency, while the advantage of the LFR is the low investment cost and the
decreased mechanical difficulties during the operation [19].

The solar dish collector is a new technology which is mainly commercialized with
systems coupled with solar Stirling engines [20]. However, there are designs with
cavity receivers with solar thermal applications [21-23]. The solar tower is a solar
concentrating technology for power production applications with high land utilization

3
[24]. The solar tower includes a tower with the absorber in its highest region and a
great field of heliostat reflectors. This technology seems to be a cost-effective one
with a relatively lower levelized cost of electricity production compared to the other
solar concentrating systems [25]. Figure 1 depicts the previous analyzed solar
concentrating technologies.

Figure 1. The most usual concentrating solar technologies

1.3 The present work

This study aims to review and to discuss the linear Fresnel reflector systems in order
to make an assessment of the existing situation. The usual and the novel design of the
LFR are examined, as well as the application of this collector type in energy systems
is investigated. Moreover, a brief comparison with the rival technology, the PTC, is
given. In the end, the future steps in the LFR technology and research are highlighted.
It is also important to state the design with Fresnel lenses is not examined in this
review paper.

2. The linear Fresnel reflector – main characteristics

2.1 The convectional LFR design
Linear Fresnel reflector is a solar concentrating technology with concentration ratio in
the range of 10 to 50. The LFR has segmented primary reflectors which are placed
close to the ground [26]. This design makes the mechanical difficulties due to wind
loads to be low and also the land utilization is low with this concentrating technology
[17]. The receiver of the LFR does not move and it is located some meters over the
ground. A typical image of an LFR is given in figure 2 [27]. It is useful to state that

4
the LFR has a lightweight supporting system which makes the collector cost to be
relatively low.

Figure 2. A typical image of a real LFR [27]

The receiver of the LFR has usually evacuated tube collector coupled to a secondary
concentrator. The secondary concentrator has a parabolic shape which is usually a
compound parabolic concentrator (CPC). Another conventional design is with a
trapezoidal cavity receiver with many tubes inside it. Figure 3 [28] shows the
conventional receivers of LFR, the trapezoidal design in figure 3a and the design with
evacuated tube coupled to a secondary concentrator in figure 3b.

Figure 3. Conventional receivers of LFR a) Multi-tube cavity receiver b) Single

tube receiver with a secondary concentrator [28]

The primary reflectors can be flat or curved. The flat reflectors are less expensive but
they introduce higher optical losses. The curved mirrors have a parabolic shape and
they can increase the overall optical efficiency. But the curved reflectors have

5
problems because of the need for curved mirrors and so their cost is increased. Figure
4 depicts both the flat and the curved design [29]. According to the results of the Ref
[29], it has been suggested that a small deflection of 2 mm is the optimal design for
the LFR primary mirrors.

Figure 4. Primary reflectors of an LFR a) flat mirrors b) curved mirrors [29]

About the working fluids of the LFR, the water/steam is a usual choice for production
of superheater of saturated steam and high pressure. This steam can be used directly
in the turbine of a Rankine cycle or for an industrial process. Moreover, thermal oils
such as Therminol VP-1 [30] are used for various thermal applications up to 400oC.
The molten salts can be also used for power production applications [31] which use
also the molten salt for storage purposes. In the work of Bellos et al. [32] found that
the operation with molten salt leads to higher thermal efficiency compared to the
operation with thermal oil and also it is highlighted that the molten salt gives the
possibility for operation in higher temperatures up to 600 oC.

2.2 Basic mathematical formulation of LFR

The basic mathematical modeling of an LFR is presented in section 2.2. Figure 5 [33]
shows a simplified design of an LFR with flat primary mirrors and this image can be
used as an example for presenting the basic mathematics of an LFR. The following
equations regard the geometrical design, as well as the thermal, exergy and optical
analysis.

2.2.1 Geometrical analysis

The total collecting aperture (Aa) is calculated as the product of the collector length
(L), of the mirror width (W0) and the number of the mirrors (N):

(1)

The total LFR width (Wtot) is calculated as below:

(2)

The parameter (W) is estimated using the number of the primary mirrors (N) and the
distance between the first mirror and start of the coordinate x-axis (DW):

6
 (3)

The focal distance of every mirror (Fi) is calculated as:

√ (4)

The position angle (φi) of every mirror can be calculated as:

( ) [ ( ) ] (5)

Figure 5. A simplified model form an LFR with flat primary reflectors [33]

2.2.2 Optical analysis

The optical efficiency (ηopt) is calculated as the product of various parameters such as
the absorber absorbance (α), the reflector reflectance (ρ), the cover transmittance (τ)
and the intercept factor (γ). Moreover, an extra parameter, the incident angle modifier
(IAM or K), is used in order to take into consideration the variation of the optical
efficiency for the different sun positions. So, it can be written:

(6)

For the proper analysis of an LFR, the solar position is expressed through the
projection of the solar incident angle (θ) in two directions. The projection of the
incident angle on the plane which is along the collector length is the longitudinal
incident solar angle (θL), while the projection of the incident angle on the vertical
plane to the solar reflectors is the transversal incident angle (θT). Figure 6 shows these
angles with details. So, the incident angle modifier (K) can be written as below:

7
 ( )
( ) (7)
( )

For the conventional LFR, the maximum optical efficiency (ηopt,max) is achieved for
zero incident angles, so it can be said that ηopt,max=ηopt(θL=0, θΤ=0). A usual way for
the IAM calculation is the factorization of it using the IAM in the longitudinal (KL)
and in the transversal (KT) directions [34]:

( ) ( ) ( ) (8)

Moreover, the definitions of the (KL) and the (KT) are the following [35]:
( )
( ) (8)

( )
( ) (9)

In the Ref. [33], Bellos and Tzivanidis have suggested some analytical expressions for
the IAMs as below:

( ) ( ) √ ( ) ( ) (10)

and

⁄
( ) ( )
√ ( ⁄ )
( ) (11)
⁄ ( )
( ) ( ) * +
√ ( )
{ ( ⁄ )

In the previous expression, the mean angle (φm) is calculated as below [33]:

⁄
(12)
√ ( ⁄ )

The critical angle (θΤ,crit) can be estimated as below [33]:

( ) (13)

The previous expression is valid for 20o < φm < 70o and 0.50 < W0/Dw < 0.95. For
more details, Ref. [33] can be advised.

The previous methodology is a general rule for estimating the IAM for a typical LFR.
The use of more detailed methods with ray tracing techniques can be applied for more
accurate calculates. In any case, it can be said that the present methodology has errors
up to 5% [33].

8
 Figure 6. Solar angle definitions in the LFR geometry [33]

At the end of the optical analysis it has to be said that the slope of every flat mirror
has to be given by the following equation, as it is also explained in figure 7:

(14)

Figure 7. Slope of every primary flat mirror in the LFR

2.2.3 Thermal analysis

The equations of this section present important parameters for the thermal analysis of
the LFR. The thermal efficiency of an LFR (ηth) is the ratio of the useful heat (Qu) to
the available solar irradiation (Q s):

9
 (15)

The available solar irradiation (Qs) is calculated as below:

(16)

The useful heat production (Qu) can be estimated using the energy balance in the fluid
volume:

( ) (17)

The thermal losses of the LFR can be calculated by the energy balance in the
absorber. More specifically, the absorbed solar irradiation (Q abs) is separated into
useful heat (Qu) and thermal losses (Qloss). So, it can be written:

(18)

The absorbed solar irradiation (Qabs) can be calculated as below:

(19)

The thermal loss coefficient of the solar collector (U L) can be used for the expression
of the thermal losses.

( ) (20)

The mean receiver temperature (Tr) is a critical parameter which determines the
thermal losses. The useful heat production is connected with the mean receiver
temperature as below:

( ) (21)

The parameter (Ahex) is the heat exchange area that the fluid comes in touch with the
absorber, the parameter (h) is the fluid heat transfer coefficient, while the parameter
(Tfm) is the mean fluid temperature. The mean fluid temperature can be calculated as
the mean value of the inlet and the outlet temperature, while the heat transfer
coefficient can be estimated using Nusselt numbers from the heat transfer theory. For
example, for the tubular receiver, the Dittus-Boelter equation [36] can be used for the
turbulent flow:

(22)

The next step after the thermal analysis can be the exergy analysis of the solar
collector. The useful exergy production of the solar collector practically shows the
maximum possible work output that can be produced if the useful heat of the solar
collector is fed to a Carnot engine. For the solar collector, the useful exergy
production (Eu), neglecting the pressure drop losses, can be written as [37]:

10
 ( ) (23)

The exergy flow of the solar irradiation (E s) is estimated using the Petela model [38]:

[ ( ) ] (24)

The exergy efficiency (ηex) can be written as:

(25)

In a recent paper [39], the use of an endoreversible cycle for the estimation of the real
electrical efficiency of solar power (ηel) cycle has been introduced. The
endoreversible cycle has been suggested by Curzon and Ahlborn [40] and it takes into
consideration the need for a temperature difference in the heat exchangers of a Carnot
power cycle.

( √ ) (26)

In the previous equations (22 to 25), the temperature levels have to be in Kelvin units.
The references temperature (T0) can be selected at 298.15 K, the sun temperature
(Tsun) at 5770 K, while the mean fluid temperature (T fm) is approximately the average
value of the inlet and outlet temperature.

2.3 Existing CSP with LFR

The use of LFR for power production has been used in many countries all over the
world. Table 1 summarizes 18 concentrating solar power plants (CSP) which have
been found according to the NREL stats [41] and the Ref [42]. The countries with
LFR CSP are China, USA, Spain, Italy, Morocco, France, Italy and India. The greater
capacity is up to 50 MWel, while the working fluids are water/steam, thermal oils and
molten salts. Four plants are under construction (U.C.), while some have stopped
operating. This situation proves a worldwide interest about the LFR technology but it
is also obvious that this technology is not well-established and many steps have to be
performed in the future.

11
 Table 1. Existing concentrating power plants with LFR [41-42]
Power Working Area Start Current
Name Country
(MWel) fluid (m2) date status
Alba Nova 1 France 12 Water/steam - 2015 -
Augustin Fresnel 1 France 0.25 Water/steam - 2012 -
Dacheng Dunhuang China 50 Molten salt - - (U.C.)
Dadri ISCC Plant India 14 Water 33000 2017 (U.C.)
Dhursar India 125 Water/steam - 2014 Operation
eCare Morocco 1 Water 10000 2010 -
eLLO France 9 Water 153000 2018 (U.C.)
FRESDEMO Spain 0.8 Water/steam - 2007 -
Huaneng China 1.5 Water/steam - 2012 -
IRESEN Morocco 1 Mineral oil 11400 2016 (U.C.)
Kimberlina USA 5 Water 25988 2008 No operation
Liddel Australia 3 Water/steam 18490 2012 No operation
Puerto Errado 1 Spain 1.4 Water 25792 2009 Operation
Puerto Errado 2 Spain 30 Water 302000 2012 Operation
Rende Italy 1 Diathermic oil 9780 2014 Operation
Urat China 50 Thermal oil - - (U.C.)
Zhangbei China 50 Water/steam - - (U.C.)
Zhangjiakou China 50 Water/steam - - (U.C.)

2.4 Comparison with PTC

The basic competitive technology of the LFR is the PTC. Both are linear
concentrating technologies which present similarities and differences. PTC and LFR
usually are compared in energy and financial terms in order to determine the most
suitable choice for every application. The similarities of these collectors are based on
the linear character of their concentrators. So, the absorbers are linear and in many
cases, the absorbers of the PTC (evacuated tubes) can be used in the LFR
configurations. The concentration ratios are in the same ranges from 10 up to 50 and
generally, the operating temperatures of both technologies can be up to 400-500oC.
The working fluids are similar and they can be water/steam, thermal oils and molten
salts.

However, the different points are many and important. Firstly, the primary
concentrator of the LFR is segmented, while the PTC has a continuous concentrator.
So, the wind loads are great in the PTC and low in the LFR [43-44]. The tracking
system of the LFR is simpler because the primary mirrors are rotated close to the
ground and there are not great movements of all the systems. Furthermore, the
receiver of the PTC is moving during its operation while the LFR is constant. This
situation makes simpler the connections in the LFR because they can be stable and not
flexible as in the PTC. So, the risks for working fluid leakage are lower something
that reduces the safety measures that have to be taken. All these facts make the LFR
be a low-cost technology compared to the PTC. Moreover, the design with the
segmented mirrors in the LFR gives the possibility of increasing the concentration
ratio without great land utilization [19].

In the efficiency comparison, the PTC presents higher thermal efficiency performance

12
than the LFR because of the important optical losses of the LFR. The segmented
primary reflectors introduce important optical losses due to blocking and shading
effecting among them [45-46]. Also, the optical end losses of the LFR are more
important than the PTC because the ratio (F/L) is greater in the LFR, the fact that
increases the shaded part of the receiver especially in low solar altitude cases [39].
Figure 8 shows the IAMs for the PTC and the LFR [39]. It is clear that the existence
of two different factors in the LFR (KL and KT) makes the overall optical efficiency of
this technology lower than the PTC which has only one factor (K). About the thermal
output, figure 9 shows that the PTC leads to higher useful thermal production during
all the year period compared to the LFR [39]. This example regards the location for
Athens (Greece) with latitude about 38o and for operation at 350oC with thermal oil.
In this case, the results of Ref. [39] proved that the PTC leads to 47% more useful
heat production compared to LFR on a yearly basis.

Moreover, it is important to state that both technologies need a single axis tracking
mechanism in order to follow properly the sun position. The LFR is always located
with the linear axis in the South-North direction while it follows the sun in the East-
West direction. This strategy is also usual in the PTC systems but the PTC can operate
with other strategies such as their axis in the East-West direction and tracking the sun
in the South-North direction, as well as with polar tracking systems.

About the cost, the LFR seems to be a less expensive technology compared to the
PTC. The investment cost of the PTC is estimated at 275 €/m2 [47-48], while the cost
of the LFR around 200 €/m2 [49]. Generally, the cost of the LFR can be found in
lower values in the literature such as in Ref [50] with the value of 175 €/m2. It is also
important to state that in all the comparative literature studies between LFR and PTC,
the cost of the LFR is always lower to the PTC, the fact that makes clear the cost
relationship between these technologies [51]. Furthermore, the operation and
maintenance costs are lower for the LFR compared to the PTC due to the smaller
movement of the concentrator and the stable receiver.

13
Figure 8. Comparison of the incident angle modifiers between PTC and LFR [39]

Figure 9. Monthly thermal production per collecting area for PTC and LFR in
the location of Athens (Greece) with the fluid temperature at 350oC [39]

14
3. Design of LFR
The LFR is a non-well-established collector and so there are numerous different
designs in the literature. The variation of the LFR configurations regards the design of
the primary concentrator, of the receiver, as well as of other design innovations. All
these points are presents in section 3.

3.1 Primary concentrator designs

The conventional design of the primary reflectors is given in figure 10a [52]. All the
mirrors have the proper inclination angles in order to concentrate properly the solar
irradiation into the receiver. The figures 10b and 10c [52] show some other
configurations with the mirrors to have alternative inclinations (compact designs) in
order to avoid blocking and shading effects. However, the results of Ref [52] proved
that the conventional design of Figure 10a leads to higher efficiency because the other
designs with alternative inclinations lead to high dispersion of the solar rays because
the mirrors are located far from the receiver.

Figure 10. Different configurations of the primary reflectors a) conventional

design b) totally alternative inclinations c) partially alternative inclinations [52]

15
Another idea about the primary reflectors is the use of an etendue-matched mirror
field as it is given in figure 11 [53]. This design belongs to compact LFR systems and
it requires an intelligent system for the proper tracking of the mirrors, something that
increases the system cost. Recently, a compact LFR has been studied experimentally
by Zhu and Chen [54] and they found that this system (see figure 12) leads to low
ground utilization at 0.95 and to a concentration ratio at 15.14.

Figure 11. Incident solar irradiation contours in [W/m2] for an etendue-matched

mirror field [53]

Figure 12. Compact LFR design with a concentration ratio of 15.14 [54]

16
The LFR and especially the system with relatively low length suffers from great end
losses and so the first part of the receiver is shaded. This situation has made many
researchers find new ways for eliminating this problem. The simpler solution is the
movement or to extend of the receiver some meter back in order to reduce the end
losses. Hongh and Larsen [55] extended the receiver some meters after the solar field,
as figure 13 illustrates. This idea is beneficial, especially the winter months where the
solar altitude is low and the optical losses are very important. Yang et al. [56]
examined a system which has a movable mirror field in the South-North direction in
order to reduce the optical losses. This idea tries to adjust the location of the mirrors
every moment in order the incident solar irradiation to the receiver to be maximized.
Figure 14 shows this idea which has been examined by Yang et al. [56]. They found
that the yearly optical efficiency can be improved from 8% up to 50%.

Figure 13. Extension of the receiver after the mirrors for end losses reduction
[55]

Figure 14. Two-axis tracking system of the mirrors with the extra movement in
the North-South direction for the elimination of the end losses [56]

17
The next part of the literature investigates system with an elevated mirror field. This
idea tries also to reduce the optical losses but with a different way than the previous
studies. Figure 15 exhibits this idea which has been examined by Pulido-Iparraguirre
et al. [57] and it can enhance the power production from 2% up to 61%. Moreover,
the authors of this work also found that the shading and blocking effects of the
mirrors are reduced with this design. This idea has been also examined by Ma and
Chang [58] and 50% thermal efficiency enhancement compared to the conventional
LFR has been found.

Figure 15. Elevated mirrors for reducing the end losses [57]

The next step is the simultaneous movements of the mirrors and of the receiver which
has been examined by Zhu et al. [59]. This idea is given in figure 16 and it has found
to be an efficient way of increasing the thermal efficiency of the system. Another idea
is the rotation of the mirrors in the East-West direction in order to reduce the optical
losses, as it is presented in figure 17 [60]. Furthermore, it has to be said about the idea
for tracking azimuth mirrors which has been studied by Huang et al. [61]. They found
mean yearly efficiency at 61% and they stated that this is greater than the performance
of the conventional LFR designs.

18
 Figure 16. Systems with mirror and receiver movement for end losses
minimization [59]

Figure 17. LFR with a mirror field which rotates in the East-West direction [60]

In the end, the studies about parabolic shape concentrators in LFR systems are given.
These systems are hybrid collectors by combining PTC and LFR. Momeni et al. [62]
studied the use of six great parabolic shape primary mirrors, as they are given in
figure 18, in order to reduce the number of primary mirrors and to reduce the tracking
complexity. The use of segmented parabola as the primary reflector of an LFR has
been studied by Zhu and Huang [63] and it is given in figure 19. They found about
8% higher thermal efficiency compared to the usual LFR system. In another work,
Zhu et al. [64] improved the previous idea by moving properly the receiver in order to
reduce the end losses. The total configuration is given in figure 20 and it is found to
be an efficient one compared to other LFRs.

19
Figure 18. Parabolic shape primary mirrors for a lower number of primary
mirrors [62]

Figure 19. Segmented parabolic shape primary concentrator [63]

Figure 20. LFR with parabolic shape primary concentrator and movable
receiver for end losses elimination [64]

20
3.2 Receiver designs
In the literature, there are numerous ideas about the possible designs of the LFR
receivers. Tubular receivers, flat receivers, cavity receivers and evacuated tubes are
usual choices for the exploitation of the incident solar irradiation from the primary
reflectors. All these designs are studied in this section.

3.2.1 Evacuated tube receivers

The use of simple tubular receivers was an initial old idea which has been studied by
the first steps in the design of the LFR receivers [65-68]. The use of evacuated tubes
for operation at high temperatures (up to 400-500oC) is the next step in the evolution
of the receivers. However, the use of single evacuated tubes does not lead to high
intercept factor and thus the use of secondary concentrators is usually preferred.
Feuermann and Gordon [69] were the first researchers who studied this idea in 1991.

So, the use of an evacuated tube receiver coupled to a secondary concentrator is an

efficient way which has been studied by many researchers. The majority of the studies
investigate compound parabolic concentrators (CPC) as the secondary concentrators
in the LFR. Figure 21 shows clearly this design where the evacuated tube is inside the
CPC cavity which is an open cavity. In this case, the existence of the tubular cover in
the absorber practically reduces the impact of the convection losses and the radiation
losses are the major reason for thermal losses. About the design of figure 21, Qiu et
al. [31] found that the maximum optical efficiency is 65% and the mean yearly optical
efficiency is ranged from 34.8% up to 55.2% for different geographical latitudes. As a
representative value of the mean yearly thermal efficiency of this system, the value of
46% can be adopted. Ma et al. [70] studied the shape LFR type and found maximum
optical efficiency at 68%. Detailed thermal loss studies about these receivers have
been conducted in Refs. [71-73].

Figure 21. Design of an LFR with an evacuated tube in the CPC secondary
reflector [31]

The next step in the literature regards the studies which try to optimize the CPC
geometry or to find alternative secondary reflector shapes. Balaji et al. [74] compared
the classical CPC with an involute geometry and they found the CPC to be a more
efficient choice. More specifically, they found that the classical CPC leads to 62.3%

21
optical efficiency while the involute to 59.5%. Bellos et al. [32] studied the use of a
simple parabolic shape geometry (no CPC) and they optimized the location of the
parabola. Finally, they found the maximum optical efficiency to be 61%, while the
maximum exergy efficiency to be around 30% for operation at 700 K with molten salt
or liquid sodium as working fluids. Grena and Tarquini [75] designed a two-wings
geometry as the secondary reflector of an LFR, as it is given in figure 22. The authors
of this work stated that this design is able to operate with higher concentration ratios
and with more uniform heat flux distribution, two critical factors for operation at high
temperatures (~550oC) with molten salts). Another idea is the use of a double CPC
receiver, as it has been suggested by Collares-Pereira et al. [76] and it is depicted in
figure 23. This is an asymmetric and compact design which has high performance and
it is a promising choice for the future LFRs, as the authors suggested.

Figure 22. A two-wings geometry for the secondary reflector of the LFR [75]

Figure 23. A double CPC receiver [76] (License Number: 4495350897034)

22
The last part of the literature studies regards comparison studies and optimization
studies about the secondary concentrators. Canavarro et al. [77] performed a
simultaneous multiple surface method for the design of the secondary reflector (see
figure 24) in order to increase the optical efficiency of the LFR. They finally found
the optical efficiency up to 70% with the optimum design and they stated that it is
greater than the conventional CPC design, but it is lower compared to the parabolic
trough collector. Zhu [78] developed an adaptive method for the proper design of the
secondary concentrator. This method is presented in figure 25 and it is able to achieve
secondary concentrator efficiency at 90%. Prasad et al. [79] optimized the CPC
geometry of the secondary reflector from the field at Vallipuram in India (see figure
26). They applied a novel segmented parabolic secondary concentrator profile in order
to optimize the secondary concentrators and they also applied the concept of variable
aim lines in the primary mirrors for creating more uniform heat flux over the
absorber. Finally, they found the maximum optical efficiency at 76.2% with the
segmented parabolic concentrator, while the CPC and the trapezoidal concentrators
have 74.9% and 70.9% optical efficiency respectively. Bellos et al. [80] suggested the
use of Bezier polynomial parameterization of the secondary reflector geometry in
order to maximize the optical efficiency. The examined methodology is based on the
movement of the control points and it is presented in figure 27. They finally found
72.84% optical efficiency with the optimum design while the initial one had 61.01%
optical efficiency. The obtained value in the optimal design seems to be high because
the primary reflectors are flat. Moreover, the authors stated that this design leads to
more uniform heat flux distribution compared to the initial one, while it has high
performance with the variation of the transversal incident solar angle.

In the end, it is useful to state about some comparative studies. Hack et al. [81] found
that the adaptive design is the best choice with 94.8% secondary concentrator
efficiency, while CPC, trapezoidal and two-wings (or butterfly) design follow with
82.1%, 81.4% and 48.5%. Abbas et al. [82] found that the adaptive geometry gives
similar results with the CPC design, while both geometries are better than the
segmented parabolic geometry. These comparative studies are important and they
indicate that the CPC design is an efficient choice and the adaptive design can be a
promising solution for a bit higher performance.

23
Figure 24. Design of the secondary concentrator with a simultaneous multiple
surface method [77]

Figure 25. Design of the secondary concentrator with an adaptive method [78]

24
 Figure 26. Different designs of Ref. [79] a) Trapezoidal concentrator b) CPC
concentrators c) Segmented parabolic concentrator

Figure 27. Optimization of the secondary concentrator using the Bezier

polynomial parameterization [80]

3.2.2 Cavity receivers

The cavity receivers are created by using a closed cavity device with the cover in the
down part and absorbing tubes inside. The cavity is usually insulated, while there is
internal air which creates convection thermal losses. These cavities have a lower cost
compared to the evacuated tubes but they have lower thermal efficiency, especially in
high temperatures. Thus, the cavity receivers are preferred in low and medium
temperatures up to 300oC. In the literature, there are different cavity designs with one
or more absorber tubes. The cavity has usually trapezoidal shape, while there are
designs with parabolic or CPC geometry. The geometry of the cavity plays an
important role on the natural convection as well as on the secondary reflections of the
solar rays.

25
The first part of the literature studies investigates configuration with one internal tube.
Singh et al. [83] examined a system with one tube and trapezoidal cavity shape, as it
is given in figure 19. They found the thermal efficiency to be up to 20.5% which is a
low value. Tsekouras et al. [84] studied a similar configuration and they found the
maximum optical efficiency up to 69.3% and thermal efficiency at 300oC close to
55.7%. The use of another geometry than trapezoidal is usual in the cases with one
tube inside the cavity. Montes et al. [85] examined the cavity receiver of figure 29a
with a CPC geometry and glass in the aperture, as in all the cavity designs. They
found that the thermal efficiency is 66.19% with thermal oil and the exergy efficiency
36.13% for inlet temperature at 293oC, while the outlet at 393oC. Beltagy et al. [27]
found that the daily performance of the cavity receiver of figure 29b is around 40%.
Ajdad et al. [86] found the yearly thermal performance of a similar configuration
around 45%.

Figure 28. Trapezoidal cavity receiver with one tube [83]

Figure 29. CPC cavity receiver with one tube a) from Ref. [85] b) from Ref. [27]

The second part of the literature includes designs with many tubes inside the cavity or
multi-tube cavity receivers. Usually, these designs have a trapezoidal cavity receiver
and the tubes are located in the upper part of the cavity. In some designs, the tubes
directly absorb the solar irradiation while in other designs there is an absorber plate
which is in front of the tubes. The majority of the designs have four to eight tubes
inside the cavity while there are some designs with two or three tubes.

Firstly, the studies with up to 4 tubes are given. Moghimi et al. [87] examined a
design with two tubes inside the cavity as figure 30 shows. Nixon and Davies [45, 88]
examined a configuration with three tubes inside a CPC cavity (see figure 31a) and

26
they found an instantaneous optical efficiency of around 60%, while the yearly was
around 49%. Moghimi et al. [89] studied and optimized a trapezoidal cavity with four
internal tubes, as it is given in figure 31b. Mokhtar et al. [90] studied a similar
configuration but without cover glass and they found maximum efficiency at 29%.

Figure 30. Trapezoidal cavity with two internal tubes [87]

Figure 31. a) CPC cavity with three internal tubes [45] b) Trapezoidal cavity
with four internal tubes [89]

27
The next step is the presentation of studies with more internal tubes (six to eight).
Singh et al. [91-92] studied the use of six tubes inside the trapezoidal cavity as it is
given in figure 32a. The maximum thermal efficiency was found around 70% for
operating at temperatures close to ambient, while for temperatures around 100 oC, the
thermal efficiency takes values close to 50%. Facao and Oliveira [93-94] also studied
a trapezoidal cavity with six tubes. Their study was mainly for the thermal loss
determination and the design is given in figure 32b. Other studies with the same
cavity design are in Refs [60, 95].

Figure 32. Trapezoidal cavity receiver with six tubes a) from Ref. [91] b) from
Ref. [94]

The use of seven tubes has been studied in Ref. [96-98] and the respective design is
given in figure 33. The thermal efficiency of this design has been found 71.1%, while
the respective PTC performance is 85.1% when the outlet temperature of the thermal
oil is 392oC. The use of eight tubes in the trapezoidal cavity has been studied by Qiu
et al. [28, 99], as well as by Sahoo et al. [100-102]. Qiu et al. [28] found that the
instantaneous thermal efficiency of this system is ranged from 48.3% up to 72.0%,
while the yearly optical efficiency is ranged from 44.7% up to 60.1%. Sahoo et al.
[100] found that the collector thermal efficiency is ranged from 68% up to 72.8%.

28
 Figure 33. Trapezoidal cavity receiver with seven tubes [96]

Figure 34. Trapezoidal cavity receiver with eight tubes [100]

3.2.3 Flat receivers

The use of flat receivers is an old idea which had been examined by the first
researchers about 1990 but it has also been revisited the last years with specific and
efficient designs for low and medium temperature applications. In 1989, Negi et al.
[103] studied the principles of a vertical flat receiver with mirrors of constant and
variable width. They generally were focused on the geometrical calculation of the
collector and they found higher concentration ration with the variable width design. In
1991, Mathur et al. [104] studied a flat horizontal receiver, a flat vertical receiver and
a tubular receiver (without a cavity). They found the highest concentration with the
tubular design and the lowest with the horizontal flat design. In 1993, Gordon and
Ries [105] studied the idea of using a secondary reflector for the absorber receiver.
The secondary reflector had a CPC part and a tailored edge-ray concentrator. They
found that the extra reflector aids the optical performance of the collector.

Later in 2016, Bellos et al. [106-107] studied experimentally and numerically an LFR
with a flat absorber. The absorber is practically an inverted flat plate collector with
flat cover, flat absorber and three tubes in the backside of the absorber plate, as it is

29
given in figure 35. Also, the total receiver is insulated in order to reduce the thermal
losses. The experiments had performed during the winter and the optical efficiency
was found about 25.5%. The encouraging point of this design is the relatively low
thermal losses which make the thermal efficiency to be around 24.5% for inlet
temperatures up to 100oC. About the same system, Mathioulakis et al. [108] found
that the IAM modifier is different for every reflector and a detailed optical
methodology is required for the suitable optical investigation of this system. Another
work with a flat receiver has been conducted by Pauletta in 2016 [109]. This work
suggested the use of a flat evacuated receiver for an LFR. The maximum efficiency
was about 65% for fluid temperature about 200oC over the ambient temperature,
while the optical efficiency is 70%.

Figure 35. Inverted flat plate collector as the receiver in an LFR [107]

3.2.4 Alternative receivers

The previous subsections 3.2.1 to 3.2.3 indicate the great interest of different LFR
receiver designs. However, there are some more alternative ideas which do not belong
to the previous classifications with evacuated tubes, cavity receivers and flat
absorbers. These alternative designs are presented in subsection 3.2.4 as below.

The first worth-mentioning idea is the use of a triangular receiver. This idea has been
suggested by Goswami in 1990 [110] and it is given in figure 36, but it has not
examined extensively by other researchers. The basic concept of this configuration is
the reduction of the peak heat flux over the absorber. Cruz-Silva et al. [111] examined
a special cavity receiver with a secondary reflector. The secondary reflector is a
dielectric totally internally reflecting concentrator and it is given in figure 17. The
concentrator efficiency was found up to 93.5% and the authors stated that this design
can be applied in a photovoltaic or thermal application. A V-cavity receiver with ten
internal tubes has been studied by Lin et al. [112] and it is depicted in figure 38. This
design has 75.5% optical efficiency but the thermal efficiency is found 45% for
operation at 90oC and 37% for operation at 150oC.

30
A double stage LFR has been studied by Li et al. [113-114]. In Ref. [113], the
receiver is a conical coil design which is located close to the ground, while the solar
irradiation reaches to this are after two-stage reflections. Figure 39 shows the
examined system in a clear way. It is found that the thermal efficiency is 60% for 81
K fluid temperature increase and 39% for 181 K temperature increase. In Ref. [114],
modifications of the previous idea have been investigated. The last alternative design
is a micro concentrating collector which is depicted in figure 40 and it has been
studied by Sultana et al. [115-116]. This is a compact system which can be applied in
rooftops and it has reduced convective losses.

Figure 36. Triangular receiver design [110]

Figure 37. Flat absorber with a dielectric totally internally reflecting

concentrator [111]

31
 Figure 38. V-cavity receiver with ten tubes [112]

Figure 39. Double stage LFR with a conical coil receiver [113]

32
 Figure 40. Micro concentrating LFR [116]

4. Applications with LFR

The LFR is a solar thermal technology which can operate in a great range of operating
temperature levels. This fact makes possible the exploitation of this technology in a
great range of applications which are described in section 4.

4.1 Power production applications

The power production applications with LFR are the majority of the studies about the
application of this technology. The majority of the studies are focused on the
comparison of LFR with PTC in order to determine the most viable technology.
Firstly, some studies which are devoted practically only to the LFR are given. Pierce
et al. [117] investigated the use of the LFR in a stand-alone and in a solar-aid
water/steam Rankine cycle for South Africa claim conditions. They found that the
optimum scenario is the use of the LFR as an aid system leads to 25% higher
electricity production than the utilization of LFR as the main primary heat source
provider. Manikumar and Arasu [118] studied a Rankine cycle with supercritical CO2
as the working fluid and they found the system electrical efficiency to be close to
10%. Moreover, the use of a steam engine coupled to an LFR for power production
has been done by Dellicompagni et al. [119].

The next step regards the comparative studies between LFR and PTC for power
production applications. Sebastian et al. [120] studied the use of different LFR
configuration to a water/steam Rankine cycle and they performed comparisons with
PTC systems. They found that the application of a novel storage strategy with three
tanks (see figure 41) is able to enhance the yearly performance of an LFR power plant
up to 10%. However, in all the cases the PTC leads to higher performance and the

33
authors stated that the novel storage strategy is able to eliminate the performance
difference between the two solar technologies. Sharma et al. [121] found that the
power plants with LFR have to be designed with greater solar multiple factors than
the PTC power plants. More specifically, they found the solar multiple ranges from
1.4 to 1.6 for PTC and from 1.8 to 2.0 for LFR. Desai et al. [122] found that the
combination of PTC with LFR, as it is given in figure 42, is the best case financially
and it is to give 9.6% lower cost of electricity compared to the plant with PTC and
13.5% lower compared to the plant with LFR.

Another important part of the literature studies examine energetically and financially
the two solar linear technologies and these studies try to estimate the critical LFR
investment cost which makes the competitive to PTC. If the LFR has lower
investment cost than the critical, then this is the most viable technology. Table 2
summarizes all the studies which give detailed parameters for cost and energy
performance.

Bellos and Tzivanidis [39] compared two commercial PTC and LFR collectors for the
climate conditions of Athens (Greece). They found that the mean IAM for the PTC is
83.73% while for the LFR is 58.66%. Moreover, the calculated the electrical
efficiency to be 16.12% for the PTC and 10.92% for the LFR on a yearly basis. The
critical cost ratio was found at 67% with the PTC cost at 275 €/m2 and the LFR cost at
185 €/m2 Moreover, they stated that the simple payback period for investment for
power production is around 8~9 years, while for a heat production around 3~4 years.
Morin et al. [47] found that the use of LFR leads to 9.3% yearly electrical efficiency,
while the use of PTC to 15% for the location of Dagget (USA). They stated that the
cost of the LFR has to be about half of the PTC in order similar financial performance
to be achieved with both technologies. Casartelli et al. [123] compared the two solar
organic Rankine cycles (ORC) for the climate conditions of Sevilla (Spain) and they
found 15.2% electrical performance with PTC and 10.1% with LFR. They also stated
that the LFR cost has to be up to 50% of the PTC cost. A similar result about the LFR
cost has been found by Giostri et al. [124] for the climate conditions of Las Vegas
(USA) They also stated that the electrical efficiency with PTC and LFR are 23.6%
and 19.25% respectively. Kumar and Reddy found that the LFR cost has to be up to
73% of the PTC cost for the climate conditions of India.

In other studies, Schenk et al. [126] stated that the LFR cost has to be ranged from
202 to 235 €/m2 in order to compete for the PTC with the cost at 300 €/m2. Cocco and
Cau [49] found that the electrical efficiency with PTC is ranged from 10.8% to
11.9%, while with LFR from 7.3% to 8.1%. They concluded that the cost of
electricity with PTC is 340 €/MWh and with LFR 380 €/MWh, while the PTC cost
was selected at 275 €/m2 and the LFR cost at €/m2. Lastly, Tola et al. [127] studied a
supercritical CO2 cycle driven by linear solar systems. They stated that if the PTC is
180 €/m2, the LFR cost has to be up to 120 €/m2 in order to be competitive
technology.

34
Figure 41. Water/steam Rankine power cycle with LFR and a storage system
with three tanks [120]

Figure 42. Power plant with PTC and LFR [122]

35
 Table 2. Comparative studies about power production between LFR and PTC.
Yearly Electrical efficiency Critical cost
Study Location potential ratio
PTC LFR
(kWh/m2) (CLFR/CPTC)
Bellos and Athens
1593 16.12% 10.92% 67%
Tzivanidis [39] (Greece)
Morin et al. [47] Dagget (USA) 2791 15% 9.3% 50%
Casartelli et al.
Sevilla (Spain) 1881 15.2% 10.1% 50%
[123]
Giostri et al. Las Vegas
2592 23.6% 19.25% 50%
[124] (USA)
Kumar and
India 1584 23.16% 12.17% 73%
Reddy [125]

4.2 Cogeneration systems

The use of LFR in cogeneration systems is usual in the literature. In all the systems,
the main useful output is the power, while the other is cooling, heating or fresh water.

Firstly, the studies for power and heating production are given Dabwan and
Mokheimer [128] studied a system with a gas turbine for electricity and stem
production (process heat). The total plant efficiency was found at 85% and the
levelized cost of electricity about €/kWh with the use of LFR. Burin et al. [129]
examined the use of a water/steam Rankine cycle with LFR which has 13% electrical
efficiency and a levelized cost of electricity between 0.16 and 0.21 €/kWh. Lopez et
al. [130] investigated a similar system and they found that the use of LFR to avoid
10% fossil fuel. Moaleman et al. [131] investigated a system for heating and power
production. A special design of LFR with a triangular receiver which has photovoltaic
cells incorporated is the studied design. They found that 600 m2 of LFR are able to
produce 39400 kWh cooling, 6528 kWh heating and 2290 kWh electricity in a year
period.

About the systems for power and fresh water production, the studies of Askari and
Ameri [132-134] take the greatest part in the literature. In Ref [132], a system with
organic Rankine cycle and distillation unit has been examined and it is depicted in
figure 43. It is found that the neat electricity production of the installation is 185.5
MWhel, the daily water production 2 x 106 m3 and the levelized cost of electricity
around 0.17 €/kWh. Soomro and Kim [135] studied a system with Rankine cycle, two
storage tanks and a distillation unit. They found the monthly electricity production to
be ranged from 11 to 38 GWh, while the daily fresh water production to be about 32
tones.

Patel et al. [136] investigated a system with ORC, vapor compression cycle and
absorption chiller for power and cooling production, as it is given in figure 44. They
found that the solar fraction with the LFR is about to 25% and the payback period is
close to 8 years. Boyaghchi and Sohbatloo [137] studied and optimized a system for
power and LNG production which presents 7.3% energy efficiency and 12.6% exergy

36
efficiency. Thomas et al. [138] studied a trigeneration system for heating, cooling and
electricity production. This system includes a water/steam Rankine cycle, an
absorption machine, an adsorption chiller and the proper heat exchangers. They found
that the electricity production of this system is about 45 kW, while the solar field is
about 600 m2.

Figure 43. Cogeneration system for power and fresh water production [131]

Figure 44. Cogeneration system for power and cooling production [135]

37
4.3 Refrigeration systems
The refrigeration applications with LFRs are based on the use of sorption machines
and more specifically of absorption chillers. Bermejo et al. [139] studied a solar
cooling system for the location of Sevilla, Spain with 75% solar coverage which is
given in figure 45. The system has a double effect absorption chiller which has a
coefficient of performance (COP) between 1.1 and 1.25, while the daily thermal
efficiency of the LFR is 35% to 40%. In a recent work, it is studied the control
strategies of a similar configuration and the authors stated that advanced methods are
needed for a solar driven refrigeration system with LFR [140].

Velazquez et al. [141] studied the use of LFR for feeding with heat and advanced
absorption cycle for about 10.6 kW cooling production. The system COP was found
0.54 and it is 17.9% higher than the conventional single effect absorption chiller.
Serag-Eldin [142] studied a system with LFR at a roof which feeds an absorption
chiller. The LFR has a design with alternative reflectors and also there photovoltaic
panels in the roof.

Figure 45. Solar cooling system with LFR and absorption chiller [139]

38
4.4 Desalination systems
The use of LFR in desalination applications for fresh water production is an idea
which has been studied by some researchers. Figure 46 shows a configuration about
this technology. Alhaj et al. [143] found that one 1 m2 of LFR produces 8.6 m3 of
fresh water on a yearly basis. Also, they stated that the use of a storage tank in the
system enhances the performance about 25%. Askari and Ameri [144] found that the
storage system is beneficial for the solar driven distillation systems and they stated
that the use of solar energy instead of fossil fuel leads to higher cost of the produced
fresh water. Sharan and Bandyopadhyay [145] performed a parametric analysis and
they suggested an optimization method for the distillation systems with solar energy
utilization.

Figure 46. Distillation application with LFR [143]

4.5 Other applications

The last part of section 4 regards miscellaneous applications which use LFR as the
heat source. In a recent general study, Dellicompagni and Franco [146] evaluated the
LFR as the primary mover for various applications. They found that the produced
useful heat from the LFR is about 243 GJ on a yearly basis. This energy can be
converted to electricity (with a power block), to fresh water (with a distillation
system) or it can be used for drying food products. They stated that the yearly fresh-
water production can be around 100 m3, while the electricity production around 1.5
GWhel.

Farooqui [147] designed an LFR which operates as a solar cooker and it is depicted in
figure 47. This system can operate at 250oC with energy efficiency up to 20% while
the exergy efficiency is up to 4%. Figure 48 shows a configuration with LFR for agri-
food processes. This system has been studied by Buscemi et al. [149] who found the
yearly contribution of the LFR to be around 40% on this process. The use of LFR for
pyrolysis purposes has been studied in Refs. [150-151]. Sanchez et al. [150] examined
the configuration of figure 49 which as an inclination of 39 o and total aperture 4.55
m2. They found that 1375 kg of biochar can be produced from 13.9 tons of biomass on
a yearly basis. Zeaiter et al. [150] found that the use of LFR is able to cover 47.14%
of the yearly needs in a pyrolysis system which operates at 550oC. In the end, it is

39
remarkable to state about the work of Barbon et al. [151] who studied an LFR with
optical fibers for lighting purposes. This configuration is given in figure 50.

Figure 47. An LFR which operates as a solar cooker [147]

Figure 48. Agri-food processes with LFR [148]

Figure 49. Pyrolysis process in an LFR [149]

40
 Figure 50. Lighting application with optical fibers and LFR [151]

5. Discussion
In this section, the previously presented studies are deeply discussed in order useful
conclusions to be extracted. Also, the future trends and the limitations of the LFR are
discussed.

5.1 Discussion of the different primary reflector designs

The conventional LFR have their linear axis in the South-North direction and they are
segmented mirrors which have their centers in a horizontal plane (approximately).
This design suffers from high optical end losses because of the high ratio (F/L). So,
many alternative designs have been studied in order to eliminate or to reduce this
problem.

One promising idea is the extension of the receiver after the mirrors end [55] in order
to exploit the solar irradiation from the end losses. The optimization of this idea has
been performed in Ref [56] with the use of moving mirrors for avoiding the use of
greater receiver length which is associated with increased cost. This idea can be an
effective way of improving the performance of the systems without high length
because these systems suffer from high optical end losses.

Another interesting idea is the use of inclined primary mirrors for reducing the
incident angle between mirrors and sun. This idea has been studied in Refs [57-58]
with important enhancements. However, the inclines mirrors can be applied in short
solar field and not in lengthy solar fields because of geometrical constraints due to the
distance of the mirrors from the ground.

Lastly, it has to be said about the use of alternative mirror designs in order to reduce
the blocking and shading optical losses. These designs are promising for LFR
compact designs but they face important problems due to the great distance between
mirror and receiver [52]. So, there is a need for a very special and optimized design.

41
5.2 Discussion of the different receiver designs
In the literature, there are numerous receiver designs about the LFR. Generally, they
can be classified into evacuated tube receivers and to cavity receivers. The evacuated
tubes are associated with a secondary concentrator and they are used in higher
temperatures than the cavities which have usually trapezoidal shape.

About the evacuated tubes, it has been found that the CPC design is the most usual
and efficient choice for the secondary reflector. The use of an adaptive method [78]
for its design or other optimization methods such as Bezier polynomial
parameterization [80] is an important techniques for achieving high optical
performance. About the cavity receivers, the use of a trapezoidal cavity with fluid
tubes in its backside is the usual design. The number of tubes is usually from 4 up to
8, while there are some designs with one, two or three tubes. The use of cover is
needed in order to reduce the convection thermal losses. Moreover, these cavities are
well-insulated in their back-side. Other alternative designs have flat receivers [107],
triangular receivers [110] or multi-stage concentrators with cavity receivers [113].

Lastly, it has to be said about the work of Montes et al. [44] who compared different
receivers with evacuated and non-evacuated receivers. They stated that the evacuated
have higher thermal efficiency in low temperatures the difference is small. So, they
suggested the use of low-quality receivers (non-evacuated) in the first modules which
operate with low temperatures in a solar field, and in the last modules to use the
evacuated tubes. This hybrid configuration can create cost-effective solar fields.

5.3 Discussion of the LFR applications

The use of LFR has been studied in various applications. The majority of the studied
regard power production, while applications of heating, cooling and fresh-water
production are also usual. There are also studies about cogeneration systems which
produce power and an extra useful product.

It has been found that the LFR is the main antagonist of the PTC and so there are
many studies which compare them energetically and financially. In Ref [39], it is
found that the LFR suffers from low optical efficiency and this fact leads to decreased
useful heat production. However, the LFR has lower specific installation cost thane
the PTC and so there is potential for more viable investments. It has been generally
found from the literature that the LFR has to be 50% to 70% of the PTC cost in order
to have an equivalent investment. So, if the specific cost of the PTC is about 275
€/m2, the LFR cost has to be lower than 200 €/m2 and maybe close to 150 €/m2 in
order to be an attractive technology. The yearly electrical to solar efficiency for a PTC
is generally around 15% while with LFR is around 10% which is low value. So, the
LFR can be a completive technology if its cost is reduced and also the optical
efficiency can be enhanced.

About the other applications, the refrigeration and the desalination systems are usually
studied with LFR. Especially the solar refrigeration systems with double effect

42
absorption chillers seem to be ideally coupled with LFR. Moreover, there are
alternative ideas such as the pyrolysis applications and the lighting applications with
optical fibers in the literature.

5.4 Future trends in LFR

The LFR is not a well-established technology and so there is a lot of research on this
field. There are numerous designs that have been studied and also there are other
ideas that can be further investigated.

About the concentrators, there is the need to study the ideas of inclined mirror field
and extended receiver more and in financial terms. About the receivers, there is a need
for a financial comparison of the system with evacuated and non-evacuated tubes.
Moreover, there is a critical need for studying thermal enhancement techniques such
as the use of nanofluids, turbulators and other ideas. Bellos and Tzivanidis [152]
found that the use of nanofluids is able to enhance the thermal efficiency of LFR up to
0.8%, while they found that the internal fins inside the absorber can lead to a bit
higher enhancement than nanofluids [153]. However, there are no other studies on this
field and this scientific gap has to be covered. More specifically, possible ideas are the
use of flow inserts (e.g. twisted tape inserts), sinusoidal inserts, internal fins, metallic
porous inserts and the use of different nanofluids (e.g. Thermal oil/CuO).

Finally, it has to be said that there is a need for conducting comparative studies
between LFR and PTC for applications such as solar cooling and desalination.
Moreover, the use of LFR for trigeneration systems have to be studied more,
especially by the financial point of view.

6. Conclusions
Linear Fresnel reflector is one of the most promising solar concentrating technologies
for medium and high-temperature applications. The objective of this work is the
review of the usual and alternative designs and applications about the LFR
technology. The found configurations are presented and discussed with details. The
most important conclusions about the LFR from this review are listed below:

- The optical end losses are the most important cause of losses in the LFR. The
extension of the receiver after the mirror end, the two axis movement of the mirrors
and the inclination mirror field are promising choices for reducing this kind of optical
loss.

- The most usual receivers are with evacuated tubes and with cavities. The evacuated
tubes are usually coupled to CPC secondary reflectors, while the cavities have cover
glass and a trapezoidal shape. The most efficient receivers are the evacuated tubes
(operation up to 500oC), while the trapezoidal cavities less expensive (operation up to
300oC).

- The LFR is usually applied for power production applications, while there are
studies about refrigeration, desalination and process heat.

43
- It is found that the cost of the LFR has to be up to 70% of the PTC cost in order to
be a financially viable investment. Also, it is found that the PTC is a more efficient
technology because of the lower optical losses.

- In the future, there is a need for more studies about the applications of the LFR and
comparative studies of different LFR designs in energetic and financial terms.

Acknowledgments
D. Evangelos Bellos would like to thank ―Bodossaki Foundation‖ for its financial
support.

Nomenclature
Aa Collector aperture, m2
Ahex Heat exchange area, m2
C Concentration ratio, -
CLFR Linear Fresnel reflector specific cost, €/m2
CPTC Parabolic trough collector specific cost, €/m2
cp Specific heat capacity, J/kgK

Dtube Tube diameter, m

DW Distance between reflectors, m
E Exergy flow, W
F Focal length, m
Gb Solar direct beam irradiation, W/m2
h Heat transfer coefficient, W/m2K

k Thermal conductivity, W/mK

K Total incident angle modifier, -
KL Longitudinal incident angle modifier, -
KT Transversal incident angle modifier, -
L Collector length, m
m Mass flow rate, kg/s

N Number of primary reflectors on the one side, -

Pr Prandtl number, -

44
Q Heat rate, W
Re Reynolds number, -
T Temperature, oC
UL Thermal loss coefficient, W/m2 K

W Width between the centers of the first and the last mirror, m
Wtot Total width, m
W0 Mirror width, m

Greek symbols
ηel Electrical efficiency, -
ηex Exergy efficiency, -
ηopt Optical efficiency, -
ηth Thermal efficiency, -
θ Solar incident angle, o
θL Longitude solar incident angle, o

θT Transversal solar incident angle, o

φ Position angle of the mirror, o
φm Mean position angle of the mirror, o
ψ Mirror slope angle, o
ω Design angle in figure 7, o

Subscripts and superscripts

abs absorbed
am ambient
crit critical
fm mean fluid

i counter of the primary mirrors (i=1…N)

in inlet
loss thermal losses
opt optical
out outlet
r receiver

45
u useful
s solar
0 reference

Abbreviations
CSP Concentrating Solar Power
IAM Incident Angle Modifier
LFR Linear Fresnel Reflector
ORC Organic Rankine Cycle

PTC Parabolic Trough Collector

U.C. Under Construction

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