Parabolic Trough Collectors are widespread in CSP applications. Their adoption is less developed in industrial heat demand applications. In the present thesis the design and test of two prototypes of PTC for the thermal loads in the range 80 - 250 °C is described. A mathematical model has also been developed to predict optical efficiency and thermal losses for any PTC. The model has been validated through comparison with the experimental results on the prototypes. Then it has been included in a custom-built simulation environment to predict yearly perfor- mances of a PTC field coupled with an industrial process heat demand. Energetic results are shown and final considerations are drawn for this application.

1. Design,Test
and Mathematical Modeling
of Parabolic Trough Solar Collectors
Ph.D. Dissertation of:
Marco Sotte
Advisor:
Prof. Giovanni Latini
Università Politecnica delle Marche
Scuola di Dottorato di Ricerca in Scienze dell’Ingegneria
Curriculum Energetica
X edition - new series
Curriculum Supervisor:
Prof. Massimo Paroncini

2. This presentation is to be considered
under GNU General Public License
If you intend to use material contained in this presentation please cite it as:
M. Sotte, 2012, “Design, Test and Mathematical Modeling of Parabolic Trough Solar Collectors”,
Ph.D. Thesis dissertation, Università Politecnica delle Marche, Ancona, Italy
If you need additional material on this subject:
marcosotte@gmail.com

3. Contents
Introduction
Design and manufacture of prototypes
PTC testing
Mathematical model of a PTC
Annual simulation of performances

4. Introduction
electric energy
55%
thermal energy
45%
1/5
data based on Italian energy consumption (source: Ministero Sviluppo Economico)

5. Introduction
industrial
61%
residential
39%
1/5
data based on Italian energy consumption
(source: Ministero Sviluppo Economico)

6. Introduction
100-200°C
= 4 Gtep
(Italy)
1/5
data based on Italian energy consumption (source: Ministero Sviluppo Economico)

7. Univpm.01: design concept
Design and Manufacture of Prototypes 2/5

8. Univpm.01 EPS-fiberglass sandwich =
all-in-one realization of the frame
and the parabolic shape
hand lay-up molding method
Design and Manufacture of Prototypes 2/5

9. Univpm.01 EPS-fiberglass sandwich =
all-in-one realization of the frame
and the parabolic shape
hand lay-up molding method
Design and Manufacture of Prototypes 2/5

10. Design and Manufacture of Prototypes
Univpm.01 EPS-fiberglass sandwich =
all-in-one realization of the frame
and the parabolic shape
hand lay-up molding method
2/5

11. Design and Manufacture of Prototypes
Univpm.01
Focal distance (F)
parabolic trough main characteristics
m
Rim angle (Φr) rad
Parabola length (Lc) m
Aperture area (Aap) m2
Sandwich thickness (t) m
0.25
π/2
2.10
1.85
0.05
2/5

12. focal distance (F)
parabolic trough main characteristics
m
rim angle (Φr) rad
parabola length (Lc) m
aperture area (Aap) m2
sandwich thickness (t) m
0.550
π/2
2.525
5.770
0.05
inner Al diameter (dri)
receiver characteristics
mm
outer Al diameter (dre) mm
inner glass diameter (dvi) mm
outer glass diameters (dve) mm
receiver surface (Are) m2
25
30
46
48
0.249
C=Aap/Are=23.17
concentration ratio
Design and Manufacture of Prototypes
Univpm.02
2/5

13. Univpm.02
focal distance (F)
parabolic trough main characteristics
m
rim angle (Φr) rad
parabola length (Lc) m
aperture area (Aap) m2
sandwich thickness (t) m
0.550
π/2
2.525
5.770
0.05
inner Al diameter (dri)
receiver characteristics
mm
outer Al diameter (dre) mm
inner glass diameter (dvi) mm
outer glass diameters (dve) mm
receiver surface (Are) m2
25
30
46
48
0.249
C=Are/Aap=23.17
concentration ratio
Design and Manufacture of Prototypes
VARTM
vacuum assisted
resin transfer molding process
2/5

14. PTC testing
Tests on Univpm.01
hydraulic circuit
test bench elements
movement system
instruments:
temperature, mass flow rate and DNI
water as working fluid
temperature range:
25-75°C
3/5

15. PTC testing
Results of the tests
3/5

16. PTC testing
Design and realization of a test bench
able to work with water and heat transfer oil
testing temperature tange 10 - 150°C
tests in compliance of standards:
- ASHRAE St. 93/2010
- UNI-EN 12975
3/5

17. Mathematical model of a PTC
Global efficiency
Optical efficiency
Thermal efficiency
and
4/5

18. Mathematical model of a PTC
Geometrical effects
(optical model)
4/5

19. Mathematical model of a PTC
Geometrical effects
(optical model)
4/5

20. Mathematical model of a PTC
Geometrical effects
(optical model)
4/5

21. Mathematical model of a PTC
- materials
- manufacture and assembly
- operation
Intercept factor
(optical model)
Random errors
Nonrandom errors (deterministc values)
and
4/5

22. Mathematical model of a PTC
Intercept factor
(optical model)
Universal error parameters
4/5

23. Mathematical model of a PTC
Thermal model - definition
4/5

24. Mathematical model of a PTC
Thermal model – remarks and implementation
- laminar, transitional and turbolent flow of the fluid
- implementation for both atmospheric and evacuated receiver
- properties of fluid and air considered as a function of temperature
- fourth order nonlinear algebraic system
- implemented both for water and heat transfer oil as circulating fluids
- iterative process for the solution of the system
4/5

25. Mathematical model of a PTC
Thermal model – results
cal
4/5

26. Mathematical model of a PTC
Thermal model – results
cal
exp
good agreement between exp and calculated efficiencies
average difference 3.82 %
max difference 14.05 %
4/5

27. Mathematical model of a PTC
Thermal model – results
cal
opt
4/5

28. Mathematical model of a PTC
Thermal model – results
4/5

29. Annual simulation of performance 5/5

30. Annual simulation of performance
Simulation results: average day of the month of november
5/5

31. Annual simulation of performance
Simulation results: monthly collected energy
5/5

32. Annual simulation of performance
total DNI
fallen in PTC
producible
useful
Simulation results: total energies
5/5

33. Annual simulation of performance
Simulation results: total energies
PES = 0.85 MJ/m2
5/5

34. Design,Test
and Mathematical Modeling
of Parabolic Trough Solar Collectors
Ph.D. Dissertation of:
Marco Sotte
Advisor:
Prof. Giovanni Latini
Università Politecnica delle Marche
Scuola di Dottorato di Ricerca in Scienze dell’Ingegneria
Curriculum Energetica
X edition - new series
Curriculum Supervisor:
Prof. Massimo Paroncini