Heat Transfer Analysis and Modeling of a Parabolic Trough Solar Receiver Implemented in Engineering Equation Solver

TLDR: In this article, the authors describe the development, validation, and use of a heat transfer model implemented in Engineering Equation Solver, which determines the performance of a parabolic trough solar collector's linear receiver, also called a heat collector element.

Abstract: This report describes the development, validation, and use of a heat transfer model implemented in Engineering Equation Solver. The model determines the performance of a parabolic trough solar collector's linear receiver, also called a heat collector element. All heat transfer and thermodynamic equations, optical properties, and parameters used in the model are discussed. The modeling assumptions and limitations are also discussed, along with recommendations for model improvement.

Figures

Table 6.1 HCE Design and Parameter Study Summary

Figure 5.5 Heat loss comparison chart between the EES HCE code and SNL AZTRAK test data for the off-sun case and Luz black chrome selective coating

Figure 6.7 a) Efficiency and b) heat loss charts for different annulus pressures and air as the annulus gas

Figure D.1 Zone definitions for the generalized zone analysis of the radiation heat loss from the receiver

Table 6.1 HCE Design and Parameter Study Summary

Figure D.3 Radiation heat loss comparison chart showing difference between modeling the radiation loss with and without the collector effects

Full text

Heat Transfer Analysis and
Modeling of a Parabolic Trough
Solar Receiver Implemented in
Engineering Equation Solver
October 2003 • NREL/TP-550-34169
R. Forristall
National Renewable Energy Laboratory
1617 Cole Boulevard
Golden, Colorado 80401-3393
NREL is a U.S. Department of Energy Laboratory
Operated by Midwest Research Institute • Battelle • Bechtel
Contract No. DE-AC36-99-GO10337

National Renewable Energy Laboratory
1617 Cole Boulevard
Golden, Colorado 80401-3393
NREL is a U.S. Department of Energy Laboratory
Operated by Midwest Research Institute • Battelle • Bechtel
Contract No. DE-AC36-99-GO10337
October 2003 • NREL/TP-550-34169
Heat Transfer Analysis and
Modeling of a Parabolic Trough
Solar Receiver Implemented in
Engineering Equation Solver
R. Forristall
Prepared under Task No. CP032000

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iii
HEAT TRANSFER ANALYSIS AND MODELING OF A PARABOLIC TROUGH
SOLAR RECEIVER IMPLEMENTED IN ENGINEERING EQUATION SOLVER
ABSTRACT
This report describes the development, validation, and use of a heat transfer model implemented in
Engineering Equation Solver (EES). The model determines the performance of a parabolic trough solar
collector’s linear receiver, also called a heat collector element (HCE). All heat transfer and
thermodynamic equations, optical properties, and parameters used in the model are discussed. The
modeling assumptions and limitations are also discussed, along with recommendations for model
improvement.
The model was implemented in EES in four different versions. Two versions were developed for
conducting HCE design and parameter studies, and two versions were developed for verifying the model
and evaluating field test data. One- and two-dimensional energy balances were used in the codes, where
appropriate. Each version of the codes is discussed briefly, which includes discussing the relevant EES
diagram windows, parameter tables, and lookup tables. Detailed EES software instructions are not
included; however, references are provided.
Model verification and a design and parameter study to demonstrate the model versatility are also
presented. The model was verified by comparing the field test versions of the EES codes with HCE
experimental results. The design and parameter study includes numerous charts showing HCE
performance trends based on different design and parameter inputs. Based on the design and parameter
study, suggestions for HCE and trough improvements and further studies are given.
The HCE performance software model compared well with experimental results and provided numerous
HCE design insights from the design and parameter study. The two design versions of the EES codes of
the HCE performance model are provided in the appendix.
ACKNOWLEDGMENTS
I would like to thank Associate Professor Sean Wright for his guidance and patience. I also would like to
thank my supervisor at the National Renewable Energy Laboratory (NREL), Hank Price, for providing
the opportunity to work on this project and his patience along the way. Further thanks go to Sandia
National Laboratories (SNL) and Kramer Junction Operating Corporation for hosting visits to witness the
solar trough in action and for providing test data to verify the software model. Finally, I would like to
thank all those people who were kind enough to take time out of there busy schedules to answer questions
I had during my work; specifically, Rod Mahoney, Tom Mancini, and Tim Reynolds of SNL; Mark
Mehos, JoAnn Fitch, Mary Jane Hale, Tim Wendelin, and Vahab Hassani of NREL; and Professor Sam
Welch of the University of Colorado at Denver (UCD).

iv
CONTENTS
Figures .............................................................................................................................viii
Tables.................................................................................................................................xi
Symbols ...........................................................................................................................xiii
Chapter
1. Introduction.................................................................................................................... 1
1.1 Background.................................................................................................................. 1
1.2 Motivation.................................................................................................................... 4
2. HCE Performance Model............................................................................................... 5
2.1 One-Dimensional Energy Balance Model ................................................................... 5
2.1.1 Convection Heat Transfer between the HTF and the Absorber................................ 8
2.1.1.1 Turbulent and Transitional Flow Cases ................................................................. 9
2.1.1.2 Laminar Flow Case ................................................................................................ 9
2.1.1.3 Annulus Flow Case ................................................................................................ 9
2.1.2 Conduction Heat Transfer through the Absorber Wall........................................... 10
2.1.3 Heat Transfer from the Absorber to the Glass Envelope ........................................ 11
2.1.3.1 Convection Heat Transfer .................................................................................... 11
2.1.3.1.1 Vacuum in Annulus .......................................................................................... 12
2.1.3.1.2 Pressure in Annulus .......................................................................................... 13
2.1.3.2 Radiation Heat Transfer ....................................................................................... 14
2.1.4 Conduction Heat Transfer through the Glass Envelope.......................................... 14
2.1.5 Heat Transfer from the Glass Envelope to the Atmosphere ................................... 14
2.1.5.1 Convection Heat Transfer .................................................................................... 15
2.1.5.1.1 No Wind Case ................................................................................................... 15

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Heat transfer analysis and modeling of a parabolic trough solar receiver implemented in engineering equation solver" ?

This report describes the development, validation, and use of a heat transfer model implemented in Engineering Equation Solver ( EES ). All heat transfer and thermodynamic equations, optical properties, and parameters used in the model are discussed. Model verification and a design and parameter study to demonstrate the model versatility are also presented. The HCE performance software model compared well with experimental results and provided numerous HCE design insights from the design and parameter study. The two design versions of the EES codes of the HCE performance model are provided in the appendix. Based on the design and parameter study, suggestions for HCE and trough improvements and further studies are given. 

Q2. What is the alternative to replacing an HCE after the vacuum has been lost?

Pumping an inert gas into the annulus space between the absorber and glass envelope could also be an alternative to replacing an HCE after the vacuum has been lost. 

Q3. What is the term used to account for incident angle losses?

An incident angle modifier term is added to account for incident angle losses, which includes trough end shading, changes in reflection and refraction, and selective coating incident angle effects. 

Q4. Why was the simplification decided to be left in place?

since the error results in the radiation heat transfer being overpredicted, it was decided to leave the simplification in place. 

Q5. Why did the DOE decide to develop an improved HCE performance model?

In conjunction with an expanded R&D effort to develop higher performance parabolic trough receivers, the National Renewable Energy Laboratory (NREL) funded by the U.S. Department of Energy (DOE) decided an improved HCE performance model was needed to meet the analysis needs of the program. 

Q6. What factors weigh in to determine the selection of the absorber pipe base material?

other factors such as material strength, corrosion properties, installation ease, coating application, and costs weigh in to determine the selection of the absorber pipe base material. 

Q7. What is the cost of using carbon steel in a vacuum?

If used in a vacuum, the steel would need to go through an expensive and timely process of removing out-gassing, which includes keeping the material in an oven at very high temperatures for days. 

Q8. What are the other options to reduce the solar incident angle effects?

other options to reduce the solar incident angle effects such as roughening the outer surface of the absorber [Duffie and Beckman 1991] or developing coatings that are less sensitive to incident angle may be beneficial. 

Q9. What is the optical loss determined by the incident angle modifier?

the total optical loss is determined by reducing the solar insolation by the effective optical efficiency, which includes the incident angle modifier term. 

Q10. What is the reason why some HCEs have higher annulus pressures?

Some HCEs in a SEGS plant are likely to have annulus pressures higher than the specified 0.0001 torr, because of manufacturing inconsistencies or hydrogen permeation (see Sections 6.3 and 6.5). 

Q11. What is the reason the model is not helpful in evaluating wind losses?

The wind is modeled as blowing normal to the receiver axis with no obstructions, so the model is not much help in evaluating actual wind losses that may occur as the wind blows from all directions and around adjacent SCAs. 

Q12. What is the reason the model is not able to evaluate the receiver radiation heat loss effects?

the model neglects the receiver radiation heat loss effects from the collector (see Appendix D), ground, and surrounding SCAs, and assumes an effective sky temperature for the radiation heat transfer loss (see Section 2.1.5.2), so studies of these effects also cannot be conducted with this model. 

Q13. What is the use of lookup tables?

The lookup tables provide an easy means for adding user-defined thermal-physical properties, or any other data needed in the equations in the code. 

Q14. What is the reason the model does not calculate initial guesses or parameter bounds?

since the model does not calculate initial guesses or parameter bounds, these values have to be manually input into the EES variable information window. 

Q15. What is the effect of the selective coating type on the energy rate component?

The selective coating type has a strong influence on each energy rate component, since each coating has different emittance and absorptance values.