Skip to main content

Advertisement

SpringerLink
Log in

Second law analysis and optimization of a parabolic trough receiver tube for direct steam generation

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

Entropy generation in the receiver tube of a parabolic trough solar collector can mainly be attributed to the fluid friction and finite temperature differences. The contribution of each of these components is investigated under different circumstances. Mass flow rates, tube diameters and operating pressures are investigated to obtain good guidelines for receiver tube and plant design. Operating pressures between 3 MPa (saturation temperature of 233.9 °C) and 9 MPa (saturation temperature of 303.3 °C) were investigated. Results show that small diameters can result in excessive fluid friction, especially when the mass flow rates are high. For most cases, tube diameters beyond 20 mm will exclusively be subject to entropy generation due to finite temperature differences, and entropy generation due to fluid friction will be small to negligible. Increasing the concentration ratio will decrease entropy generation, due to a higher heat flux per unit meter. This will ultimately result in shorter receiver tube lengths. From a simulated annealing optimization it was seen that if the diameter is increased, the entropy generation can be lowered, provided that the concentration ratio is kept constant. However, beyond a certain point gains in minimizing the entropy generation become negligible. The optimal operating pressure will generally increase if the mass flow rate is increased. Finally it was seen that higher operating pressures are more advantageous when the entropy generation minimization is considered in conjunction with the work output.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Abbreviations

A :

Area (m2)

A s :

Tube exposed heat transfer area (m2)

C R :

Concentration ratio

D :

Diameter (m)

E :

Exergy (W)

f :

Friction factor

\(\dot{G}\) :

Mass velocity (kg/m2 s)

h :

Heat transfer coefficient [W/(m2 K)]

I b :

Solar beam radiation (W/m2)

k :

Thermal conductivity [W/(m K)]

L :

Length (m)

\(\dot{m}\) :

Mass flow rate (kg/s)

Nu :

Nusselt number

P :

Pressure (Pa)

Pr :

Prandtl number

Q :

Heat (W)

Re :

Reynolds number

S gen :

Total entropy generation (W/K)

S gen,dT :

Entropy generation due to finite temperature differences (W/K)

S gen,dP :

Entropy generation due to fluid friction (W/K)

S r :

Reflected solar energy (W/m2)

T :

Temperature (°C or K)

V :

Velocity (m/s)

W a :

Aperture area (m)

x :

Quality (% or fraction)

ε :

Emissivity

ε void :

Void fraction

η opt :

Optical efficiency (%)

μ :

Dynamic viscosity (kg/m s)

v :

Local specific volume (m3/kg)

ρ :

Density (kg/m3)

σ :

Stefan–Boltzmann constant [W/(m2 K4)]

Φ2 :

Two-phase flow multiplier

amb :

Ambient

cb :

Convective boiling

cond :

Conduction

conv :

Convection

des :

Destroyed

fluid :

Working fluid

G :

Vapour

g :

Glass

gi :

Glass inner

go:

Glass outer

in :

Inlet

L :

Liquid

nb :

Nucleate boiling

out :

Outlet

r :

Receiver

rad :

Radiation

ri :

Receiver inner

ro :

Receiver outer

sky :

Effective sky

sun :

Apparent sun

tp :

Two-phase

wind :

Wind

References

  1. Eck M, Zarza E, Eickhoff M, Rheinländer J, Valenzuela L (2003) Applied research concerning the direct steam generation in parabolic troughs. Sol Energy 74:341–351

    Article  Google Scholar 

  2. Price H, Lüpfert E, Kearney D, Zarza E, Cohen G, Gee R, Mohoney R (2002) Advances in parabolic trough solar technology. J Sol Energy Eng 124:109–125

    Article  Google Scholar 

  3. Liu QB, Wang YL, Gao ZC, Sui J, Jin HG, Li HP (2010) Experimental investigation on a parabolic trough solar collector for thermal power generation. Sci China Tech Sci 53:52–56

    Article  Google Scholar 

  4. Odeh S, Morrison G, Behnia M (1998) Modelling of parabolic trough direct steam generation solar collectors. Sol Energy 62:395–406

    Article  Google Scholar 

  5. Forristall R (2003) Heat transfer analysis and modelling of a parabolic trough solar receiver implemented in engineering equation solver. Technical Report; National Renewable Energy Laboratory

  6. Roesle M, Coskun V, Steinfeld A (2011) Numerical analysis of heat loss from a parabolic trough absorber tube with active vacuum system. J Sol Eng 133:1–5

    Google Scholar 

  7. Koroneos C, Spachos T, Moussiopoulos N (2003) Exergetic analysis of renewable energy sources. Renew Energy 28:295–310

    Article  Google Scholar 

  8. Singh N, Kanshik S, Misra R (2000) Exergetic analysis of a solar thermal power systems. Renew Energy 19:135–143

    Article  Google Scholar 

  9. Bejan A (1996) Entropy generation minimization: the method of thermodynamic optimization of finite size systems and finite time processes. CRC Press, Boca Raton

  10. Ratts E, Raut A (2004) Entropy generation minimisation of fully developed internal flow with constant heat flux. J Heat Transf 126:656–659

    Article  Google Scholar 

  11. Sahin A (2000) Entropy generation in turbulent liquid flow through a smooth duct subjected to constant wall temperature. Int J Heat Mass Transf 43:1469–1478

    Article  MATH  Google Scholar 

  12. Revellin R, Lips S, Khandehar S, Bonjour J (2009) Local entropy generation for saturated two-phase flow. Energy 34:1113–1121

    Article  Google Scholar 

  13. Barlev D, Vidu R, Stroewe P (2011) Innovations in concentrated solar power. Sol Energy Mat Sol Cells 95(27):3–25

    Google Scholar 

  14. Gnielinsky V (1976) New equations for heat and mass transfer in turbulent pipe and channel flow. Int Chem Eng 1(2):350–367

    Google Scholar 

  15. Petukhov B (1970) Heat transfer and friction in turbulent pipe flow with variable physical properties. Adv Heat Transf 6:503–564

    Article  Google Scholar 

  16. Wojtan L, Ursenbacher T, Thome J (2005) Investigation of flow boiling in horizontal tubes part 1: a new diabetic two-phase flow pattern map. Int J Heat Mass Transf 48:2955–2969

    Article  Google Scholar 

  17. Wojtan L, Ursenbacher T, Thome J (2005) Investigation of flow boiling in horizontal tubes part 2: development of a new heat transfer model for stratified-wavy, dryout and misty flow regimes. Int J Heat Mass Transf 48:2970–2985

    Article  Google Scholar 

  18. Kattan N, Thome JR, Favrat D (1998) Flow boiling in horizontal tubes: part 1—development of a diabatic two-phase flow pattern map. J Heat Transf 120:140–147

    Article  Google Scholar 

  19. Zürcher O, Favrat D, Thome JR (2002) Evaporation of refrigerants in a horizontal tube: an improved flow patter dependent heat transfer model compared to ammonia data. Int J Heat Mass Transf 45:303–317

    Article  Google Scholar 

  20. Churchill S, Bernstein M (1977) A correlating equation for forced convection from gases and liquids to a circular cylinder in cross-flow. J Heat Transf T ASME C 99:300–306

    Article  Google Scholar 

  21. Kalogirou S (2009) Solar energy engineering: processes and systems. Elsevier, Amsterdam

  22. Garcia-Valladares O, Velázquez N (2009) Numerical simulation of parabolic trough collector: improvement using counterflow concentric circular heat exchangers. J Heat Mass Transf 52:597–609

    Article  MATH  Google Scholar 

  23. Thome J (2004) Wolverine tube heat transfer data book III. Wolverine Tube Inc. http://www.wlv.com

  24. Friedel F (1979) Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. European two-phase flow group meeting, Ispra, Italy, Paper E2

  25. Coolprop BI (2013) http://coolprop-sourceforge.net

  26. Python Software Foundation. Python (2011) http://www.python.org/doc/

  27. Scipy Community. Scipy (2011) http://docs.scipy.org/doc/

Download references

Acknowledgments

We would like to thank the University of Pretoria, University of Stellenbosch, NRF, TESP, SANERI/SANEDI, CSIR, EEDSM hub and NAC for the funding during the course of this work.

Author information

Authors and Affiliations

  1. Department of Mechanical and Aeronautical Engineering, University of Pretoria, Private Bag X20, Hatfield, 0028, South Africa

    H. C. Nolte & J. P. Meyer

  2. Department of Mechanical Engineering, University of Cape Town, Private Bag X3, Rondebosch, 7701, South Africa

    T. Bello-Ochende

Authors
  1. H. C. Nolte
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Bello-Ochende
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. P. Meyer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Bello-Ochende.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nolte, H.C., Bello-Ochende, T. & Meyer, J.P. Second law analysis and optimization of a parabolic trough receiver tube for direct steam generation. Heat Mass Transfer 51, 875–887 (2015). https://doi.org/10.1007/s00231-014-1465-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-014-1465-3

Keywords

Search

Navigation