Modular Linear Fresnel Reflecting Solar Concentrator
for Low Enthalpy Processes
O. A. Jaramillo 1, J. O. Aguilar 2, R. Castrejón-García 3, N. Velázquez 4
1- Instituto de Energías Renovables, Universidad Nacional Autónoma de México,
Privada Xochicalco s/n, Temixco, Morelos 62580, Mexico.
2- División de Ciencias e Ingeniería, Universidad de Quintana Roo,
Boulevard Bahía s/n, Quintana Roo 77019, Mexico.
3- Dirección de Desarrollo Tecnológico,, Instituto Nacional de Astrofísica, Óptica y Electrónica,
Luis Enrique Erro # 1, Tonantzintla, Puebla, 72840, México.
4- Instituto de Ingeniería, Universidad Autónoma de Baja California,
Blvd. Benito Juárez y Calle de la Normal s/n, Mexicali, Baja California 21280, Mexico.
Abstract
One of the aims of solar-thermal engineering is to develop “medium temperature collectors” in the
range of 70250 °C that are suitable for applications such as cleaning, drying, evaporation, distillation,
pasteurization, sterilization, cooking, among others, as well as applications with low temperature heat
demand and high consumption rates (domestic hot water, space heating and swimming pool heating),
and heat-driven refrigeration and cooling. In this work we present an applied research for the
development of a Modular Linear Fresnel Reflecting Solar Concentrator (MLFRC) for heating water
and steam generation at low-enthalpy in the temperature range of 70-110 °C. We present a simple
mathematical method to determine the distance among the reflecting elements and the angle for each
one in order to avoid shading between the elements during the period of operation. We designed a
non-imaging CPC cusp-type with a cylindrical receiver as a secondary concentrator. We evaluated
also the thermal performance of MLFRC according to the Standard ANSI/ASHRAE 93:2003.
Keywords: Modular Linear Fresnel Concentrator, Water and steam at low-enthalpy, Concentrated
solar energy.
1.
Introduction
Development of linear Fresnel technology has been carried out during several decades. The first
meaningful linear Fresnel collector was patented and prototyped by Francia in Italy in 1964 [1]. An
innovative commercial prototype based on the Linear Reflector technology was made by Solar Heat
and Power Company [2]. Due to the demand for renewable energy to play a significant role in the
utility-scale power supply market, current linear Fresnel technology is being targeted at hightemperature power cycles. Solar plants utilizing linear Fresnel technology have been commercially
tested and/or deployed on a utility scale around the world [3]. Currently, Novatec Solar [4] and Areva
Solar [5] are leaders in the development of high-temperature linear Fresnel collector. But also some
studies have been addressed on low or medium-temperature heat generation, given that this
technology has wide applications in building cooling and heating, industrial process, water treatment,
etc. [6-7]. A complete discussion about history, state of the art, and future of this technology can be
found in reference [8].
This work presents the design and evaluation of a Modular Linear Fresnel Reflecting Solar
Concentrator (MLFRC), which was designed to obtain hot water and low enthalpy steam at 1.5 atm in
the range of 70-110 °C. The MLFRC utilizes an array of low-profile flat reflectors and a mobile receiver
assembly that includes one linear receiver tube and a secondary concentrator. The prototype was
evaluated according to the ANSI/ASHRAE 93:2003 [9], since this standard is widely known and
provides test methods for determining the thermal performance of solar energy concentrators that use
single-phase fluids and have no significant internal energy storage. During the evaluation of MLFRC
both the thermal efficiency and the time constant for heating and cooling were obtained.
2.
Design of the MLFRC
MLFRC prototype has a rim angle of 45°, a length of 2.44 m and an aperture area close to 5 m 2. The
frame is made by using structural steel hollow sections, conventional flat mirrors are assembled to the
frame, and a mobile compound parabolic concentrator made in aluminium is used as a secondary
1
Corresponding author. Fax: +52 777 325 0018.
E-mail addresses: ojs@ier.unam.mx, oajaramillo@gmail.com (Oscar Jaramillo).
concentrator (see fig. 1). In the construction of the MLFRC, there was no need for sophisticated
machinery or skilled labour; and only hand tools were required for its assembly. Since the MLFRC is
for low enthalpy steam generation and hot water supply, it was designed with an unshielded receiver
in order to reduce both production and transportation costs. A simple solar tracking system is
employed when the concentrator is operated in a North-to-South direction.
Fig.1. Modular linear Fresnel reflecting solar concentrator
In order to perform the optical design of MLFRC the following assumptions were made:
 All reflecting surfaces are specular and free from deformations.
 Each reflector is pivoted at the centre of its longitudinal axis.
 The movement axes of each reflector are in the same plane.
 Reflecting elements do not shade each other during the period of operation from 9:00 to 15:00h
(solar time).
 4.65 mrad and it is independent of the atmospheric
 The solar acceptance angle is   32′
conditions.
 The sun passes through the zenith.
 All mirror elements have equal width W and constant length l .
 The system employs a non-imaging CPC cusp-type collector as a secondary concentrator.
Figure 2 shows a schematic drawing of the geometry of MLFRC where the reflecting elements have
same width and their movement is pivoted at the centre of its longitudinal axis.
Fig. 2. Schematic representation of the geometry of MLFRC.
The angle i of each reflecting element is calculated for redirecting the direct radiation (that arrives
with an angle  ) towards the focal plane that is located at a distance f from the reflecting element
placed in the centre of MLFRC. Considering the initial conditions of operation at 9:00 am (  s  45 ° ):
(1)
L0  0
0  22 .5°
(2)
As shown in Fig. 2, right side reflectors are closer to the horizontal position, while the left side the
elements are closer to the vertical one. Note that the elements of the left side of Fig. 2 exhibit greater
shadow projection than the elements on the right side, this is due to the inclination of the reflectors
themselves. In order to calculate the distance Li among elements and their angles i , we used a set
of equations that were taken and modified from reference [10], namely,
i 
L
  s
1
W  sin i 1  sin i

 
arctan  i 1 

cos


cos

i

1
i

2
2 f  tan90 °   s   
 2
 f
(3)
 sin i 1  sin i



(4)
 tan90 °       cos i 1  cos i 
s


where f is the focal distance, W is the width of the reflecting element and n the number of reflecting
elements of the left side of MLFRC left as shown in Fig.2. Equations (3-4) are solved iteratively for
1  i  n taking into account the initial conditions, Eqs. (1) and (2).
Li  Li 1 
W
2
By symmetry, the spacing among the reflecting elements on the left side is the same as the spacing of
the right side of MLFRC, that is to say:
Ll  Lr
(5)
while the determination of the angles of the reflecting elements on the right side are determined by
r 
 s  arctan

Lr
f
(6)
2
where the subscript is established as 1  r  n .
To determine the width of a receiving plane is considered the last element of the left side of MLFRC as
shown in Fig. 3. The width R pl is calculated as:
Rpl  rl  rc  rr
(7)

L

 L  
W

 
rl   f  sin n   tan arctan  n      tan arctan  n   

2

 
 f

 f   

(8)
where

 L 
rc  W cos n  W sin n tan arctan  n  
 f 


 L 
L
 
W

 
rr   f  sin n   tan arctan  n    tan arctan  n     
2

  
 f 
 f
  

(9)
(10)
The width R pl must match with the width of the secondary concentrator. For example, in this work we
considered the using of a non-imaging CPC cusp-type as a secondary concentrator that is shown in
Fig. 3.
In a non-imaging CPC cusp-type with a cylindrical receiver, the radius, R and the acceptance half
angle,  C , the distance,  , along a tangent from the receiver to the curve, are related to the angle 
(outlined between the radius to the bottom of the receiver and the radius to the point of tangency, T ),
by the following expressions for the two sections of the curve [11].
  R ,    c 



  R

2

  c  2  cos   c  
, c      3   c

1  sin    c 
2
2

(11)
(12)
The two expressions for    are equivalent at point P (see Fig. 3), where    c  2 . The curve is
generated by incrementing  , calculating  , and then calculating the coordinates, X and Y , by the
following expressions [11],
X  R sin    cos 
(13)
Y   R cos    sin 
The coordinate X e at the end of the Cusp-CPC is the half of rc plus the distance of ri , that is:
r
X e  c  rl
2
On the other hand, it is possible to use the following set of coupled equations to calculate the
R of the cylindrical receiver,
rc
 3

 3

 rl  R sin
  c    e cos
 c 
2
 2

 2

3

3





Ye   R cos
  c    e sin
 c 
 2

 2


 2  cos 32  2 c
 1  sin 3  2 c
2

 e  R


 
(14)
radius
(15)
(16)
(17)


Equations (15-17) is a system with three equations and three unknowns ( R , Ye and  e ), where Ye and
 e are the extreme values in the Cups-CPC geometry as shown in Fig. 3.
Fig.3. Parameters involved in the design of the Cusp-CPC
Figure 3 shows a full, un-truncated curve, which is the mathematical solution for a reflector shape with
the maximum possible concentration ratio. The total concentration ratio C for the MLFRC, including the
secondary reflector is established by the ratio between the aperture area Aa and the receptor area Ar ,
 n
 W cosi   s


2

A
 i 1
C a 
Ar
R  l

 
l

n
s 

 W cos  2 
i

i 1
R
Fig 4. Simulation of the MLFRC by using Sol TracePro.
(18)
One important aspect of the linear Fresnel collector is the optical characterisation, which was
performed by using the simulation software TracePro [12]. Considering the path of each ray interacting
with the reflecting surfaces of the collector, the flux energy arriving on the absorber can be thus
obtained. To carry out the ray tracing simulation process, a 3D model of the concentrator and cavity
receiver system was firstly established in CAD and then transferred to the TracePro, where the
surface properties like reflectivity  and absorptivity  were set into the simulation process. Figure 4
shows the results of the ray tracing method implemented in the simulation software TracePro. As can
be noted, the reflecting elements do not shade each other and the secondary concentrator collects the
solar beam in the receiver tube. The main results of design MLFRC are reported in Table 1.
Table 1. Key features of MLFRC.
i
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
3.
Ψi
45.0°
43.7°
42.3°
40.8°
39.2°
37.4°
35.6°
33.6°
31.5°
29.3°
27.0°
24.8°
22.5°
Li
-99.96cm
-91.44cm
-82.92cm
-74.41cm
-65.92cm
-57.46cm
-49.04cm
-40.66cm
-32.35cm
-24.11cm
-15.96cm
-7.92cm
0.0cm
i
1
2
3
4
5
6
7
8
9
10
11
12
Ψi
20.2°
17.9°
15.7°
13.5°
11.4°
9.4°
7.5°
5.8°
4.2°
2.7°
1.3°
0.0°
Li
7.92cm
15.96cm
24.11cm
32.35cm
40.66cm
49.04cm
57.46cm
65.92cm
74.41cm
82.92cm
91.44cm
99.96cm
Parameter
W=
f=
C=
rc =
rl =
rr =
c =
R=
e=
P(X,Y) =
P(Xe,Ye) =
ρ=
α=
Value
6.00cm
99.96cm
20.87
8.49cm
0.47cm
0.45cm
45°
1.06cm
7.73cm
(2.52,-1.02)
(4.72,6.23)
0.9
0.95
Thermal performance of MLFRC
The thermal performance of MLFRC was evaluated experimentally according to the ANSI/ASHRAE
93:2003 standard [9]. The evaluation was performed to determine the time constant and the thermal
instantaneous efficiency using water as the thermal fluid at a flow rate of 5 litres per minute. During
evaluation a direct solar radiation of 876 W/m² was measured.
3.1
Time Constant
The collector time constant is the time required for the fluid leaving the MLFRC to attain 63.2% of its
steady-state change following change in irradiance. This parameter determines the time response of
the solar collector in order to be able to evaluate the transient behaviour of the collector and select the
correct time intervals for the quasi-steady-state or steady-state efficiency tests. Figure 5 illustrates the
exponential nature of heating and cooling time and the time constants are reported in Table 2.
Table 2. The time constant for heating and cooling of MLFRC.
Time constant
Cooling
18.0 s
Heating
14.5 s
Fig. 5. Evaluation of the time constant of MLFRC.
3.2
Thermal efficiency
The ANSI/ASHRAE 93:2003 standard [9] requires efficiency tests to be run for a period equal to one
time constant or 5 minutes, whichever is larger. The thermal instantaneous efficiency  g was
evaluated experimentally by considering a time period of 5 minutes:

m C P To  Ti 
g 
Aa Gb
(19)

where Ti and To are the inlet and outlet temperatures, respectively, m is the mass flow rate, C P
is the specific heat, Aa is the aperture area of collector, and Gb is the direct solar irradiance
component in the aperture plane of the collector. The inlet temperature Ti is restricted to an interval
occurring from 20°C to 90 °C in order to avoid the phase change in the water that is used as thermal
fluid.
On the other hand, the thermal efficiency of the concentrators from the First Law is given by,

U  T  

 I  FR o  L 
(20)
C  Gb  

where T  Ti  Ta is the temperature rise across the receiver, and Ta is the ambient temperature.
Note that Eq. (20) has the form y  b  mx , which can help to experimentally obtain the heat removal
factor FR and the overall heat loss coefficient U L . Note that FRU L / C is the slope of the line and
FRo is the y-intercept. It is important to indicate that for a collector operating under steady irradiation
and fluid flow rate, FR o and FRU L / C are nearly constant. Therefore, Equation (20) plots as a straight
line on a graph of efficiency versus the heat loss parameter T / Gb
The efficiency curve for MLFRC is shown in Fig. 6. The points show the thermal instantaneous
efficiency and a straight line of best fit can be drawn between those points to obtain the thermal
efficiency for the solar concentrators. Note that the linear fit instead of a 2nd degree fit is acceptable in
the present case involving solar concentrators with low temperature. The values of the thermal
efficiency  I , the heat removal factor FR , and the overall heat loss coefficient U L are reported in
Table 3.
Tabla 3. Thermal performance of MLFRC
o [-]
I [-]
m [l /min ]
C [-]
FR [-]
UL [ W /m²K ]
FRo [-]
FRUL/C [W /m²K ]
0.54
I=(0.43977±0.00895) –(1.8306±0.19805) (t/Gb)
5.0
20.87
0.81
47.16
0.43977
1.8306
Fig. 6. Thermal efficiency data and best fit curve for the MLFRC.
Conclusions
We designed, developed, and evaluated a Modular Linear Fresnel Reflecting Solar Concentrator with
a rim angle of 45°, an aperture area close to 5.0 m 2, and a concentration ratio close to 20. The
materials used in its construction and the method of manufacture are cheap and do not require
complex manufacturing systems. The frame is made using structural steel hollow sections,
conventional flat mirror reflector strips are assembled to the frame, and a compound parabolic
concentrator made in aluminium was used as a secondary concentrator. In the construction of the
MLFRC, there was no need for sophisticated machinery or skilled labour; and during the assembly,
only hand tools were required. Since the MLFRC is for low enthalpy steam generation and hot water, it
was designed with an unshielded receiver in order to reduce both production and transportation costs.
A simple solar tracking system is employed when it is oriented in a North-to-South direction.
In order to determine the dimension of the MLFRC a simple mathematical method was developed on
the basis of simple geometrical optics, and an on-imaging CPC cusp-type with a cylindrical receiver
was designed and developed as a secondary concentrator to increase the concentration ratio of the
MLFRC. In order to evaluate the optical performance of the MLFRC a ray tracing simulation process
was implemented in the software TracePro. Results of the simulation show that the reflecting elements
do not shade each other and the secondary concentrator collects the solar beam on the receiver tube
with an optical efficiency estimated close to 54%.
The thermal performance of the MLFRC was tasted on the basis of ANSI/ASHRAE 93:2003 standard.
Peak efficiency close to 45% was assessed. The efficiency curve was established as a straight line
on the basis of the best fit for the thermal instantaneous efficiency.
Our results show that the MLFRC provides an adequate thermal efficiency and enough structural
resistance. Because of its modular design, several MLFRC can be connected in series, providing an
increment in the thermodynamic availability of the fluid. Given the geographical position of Mexico,
solar heat for industrial processes are very promising.
Acknowledgements
The authors thank José de Jesús Quiñones Aguilar, Jorge Alejandro Monreal Cruz and Álvaro Junior
Cepeda Cifuentes for their technical assistance in the development of the device and evaluation. We
thank also Dr. Maximiliano Valdez González for their technical support in the network management
and software implementation. This work was supported by PAPIIT-UNAM under the project IT100514.
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