Skip to main content
SpringerLink
Log in

Hybrid Ray Tracing Model and Particle Swarm Optimization for the Performance of an Internally Reflecting Solar Still with a Booster Reflector

  • Research Article-Mechanical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

The existing models for analyzing internally reflecting solar stills with external boosters are based on simple geometric relationships and are therefore not adequate for simulating and optimizing more complex arrangements. Therefore, this study presents a 3D hybrid ray-tracing-based model for designing and optimizing such stills. To validate the model, a geometrical arrangement was simulated, and a comparison was made with the output of a geometrical modeling package. To statistically sample a large number of solar rays to determine the irradiance received by the basin, the Latin hypercube sampling technique was used. A comparison was made with the results from a still with the same geometry but without the booster reflector. The model was then used to produce optimal optical-irradiance performance values for aspect ratio, cover angle, booster length ratio and booster angle. The effects of changing these parameters were shown using contour plots. Particle swarm optimization was then applied as an alternative method and was found to optimize the design in significantly less time.

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

Similar content being viewed by others

Abbreviations

\( A \) :

Area of basin (m2)

\( A_{\text{s}} \) :

Area of all surfaces of still (m2)

\( c_{1} ,c_{2} ,c \) :

Learning rates

\( \hat{D} \) :

Direction of propagating ray

\( F \) :

Performance factor

\( g \) :

Number of reflections

\( gBest \) :

Best solution of all particles

\( H \) :

Position of particle

\( h_{1} \) :

Height of back wall (m)

\( h_{2} \) :

Height of front wall (m)

\( I'' \) :

Irradiance at the basin (W/m2)

\( I_{\text{N}}^{''} \) :

Direct irradiance normal to the surface (W/m2)

\( i \) :

Particle number

\( j \) :

Iteration number

\( k \) :

Surface

\( L \) :

Still length (m)

\( \hat{L} \) :

Vector representing the direction of the incident ray

\( L_{\text{b}} \) :

Booster length (m)

\( N \) :

Number of samples generated in LHS

\( \hat{N} \) :

Normal vector to the surfaces

\( n \) :

Number of rays the basin received

\( \hat{N}_{\text{basin}} \) :

Normal vector to basin

\( P^{*} \left( {x^{*} ,y^{*} ,z^{*} } \right) \) :

Source coordinate of the propagating ray

\( P_{o} \left( {x_{o} ,y_{o} ,z_{o} } \right) \) :

Point chosen on still surface for backward ray tracing

\( P_{t} \left( {x_{t} ,y_{t} ,z_{t} } \right) \) :

Coordinate of intersection of ray and surface

\( P_{\infty } \left( {x_{\infty } ,y_{\infty } ,z_{\infty } } \right) \) :

Distant point for forward ray tracing

\( pBest \) :

Best solution of a particle

\( r \) :

Aspect ratio

\( r_{\text{b}} \) :

Booster length ratio

\( r_{1} ,r_{2} \) :

Random numbers (used in PSO)

\( \hat{S} \) :

Direction vector for the incoming ray

\( t \) :

Parameter to represent the intersection of ray and surface

\( t_{\infty } \) :

Parameter to obtain distant point (large value)

\( V \) :

Velocity of particle

\( W \) :

Still width (m)

\( W_{o} \) :

Instruction factor

\( \alpha_{\text{b}} \) :

Absorptivity of basin

\( \beta \) :

Cover angle (°)

\( \beta_{\text{b}} \) :

Booster angle (°)

\( \gamma \) :

Azimuthal angle of incoming ray (°)

\( \gamma_{\text{s}} \) :

Azimuthal angle of sun (°)

\( \phi \) :

Altitude angle of incoming ray (°)

\( \phi_{\text{s}} \) :

Altitude angle of sun (°)

\( \rho \) :

Reflectivity of surfaces

\( \theta \) :

Angle of incidence (°)

\( \tau \) :

Transmittivity of glass cover

References

  1. Kaviti, A.K.; Yadav, A.; Shukla, A.: Inclined solar still designs: a review. Renew. Sustain. Energy Rev. 54, 429–451 (2016)

    Article  Google Scholar 

  2. Eltawil, M.A.; Zhengming, Z.; Yuan, L.: A review of renewable energy technologies integrated with desalination systems. Renew. Sustain. Energy Rev. 13(9), 2245–2262 (2009)

    Article  Google Scholar 

  3. Ibrahim, A.G.; Elshamarka, S.E.: Performance study of a modified basin type solar still. Sol. Energy 118, 397–409 (2015)

    Article  Google Scholar 

  4. El-Swify, M.E.; Metias, M.Z.: Performance of double exposure solar still. Renew. Energy 26(4), 531–547 (2002)

    Article  Google Scholar 

  5. Al-Hayeka, I.; Badran, O.: The effect of using different designs of solar stills on water distillation. Desalination 169(2), 121–127 (2004)

    Article  Google Scholar 

  6. Al-Karaghouli, A.; Minasian, A.: A floating-wick type solar still. Renew. Energy 6(1), 77–79 (1995)

    Article  Google Scholar 

  7. Shanmugan, S.; Rajamohan, P.; Mutharasu, D.: Performance study on an acrylic mirror boosted solar distillation unit utilizing seawater. Desalination 230(1–3), 281–287 (2008)

    Article  Google Scholar 

  8. Tanaka, H.: Experimental study of a basin type solar still with internal and external reflectors in winter. Desalination 249(1), 130–134 (2009)

    Article  Google Scholar 

  9. Khalifa, A.; Ibrahim, H.: Effect of inclination of the external reflector on the performance of a basin type solar still at various seasons. Energy Sustain. Dev. 13(4), 244–249 (2009)

    Article  Google Scholar 

  10. Tanaka, H.; Nakatake, Y.: Theoretical analysis of a basin type solar still with internal and external reflectors. Desalination 197(1–3), 205–216 (2006)

    Article  Google Scholar 

  11. Cheng, Z.D.; He, Y.L.; Cui, F.Q.; Du, B.C.; Zheng, Z.J.; Xu, Y.: Comparative and sensitive analysis for parabolic trough solar collectors with a detailed Monte Carlo ray-tracing optical model. Appl. Energy 115, 559–572 (2014)

    Article  Google Scholar 

  12. Rehman, N.: Optical-irradiance ray-tracing model for the performance analysis and optimization of a façade integrated solar collector with a flat booster reflector. Sol. Energy 173, 1207–1215 (2018)

    Article  Google Scholar 

  13. Tripathi, R.; Tiwari, G.N.: Performance evaluation of a solar still by using the concept of solar fractionation. Desalination 169(1), 69–80 (2004)

    Article  Google Scholar 

  14. Rehman, N.: Optical-irradiance ray-tracing model for the performance analysis and optimization of a single slope solar still. Desalination 457, 22–31 (2019)

    Article  Google Scholar 

  15. Rehman, N.: Performance analysis and optimization of an internally reflecting single slope solar still using an optical-irradiance ray-tracing model. Desalination 472, 114181 (2019)

    Article  Google Scholar 

  16. Chan, Y.; Tzempelikos, A.: A hybrid ray-tracing and radiosity method for calculating radiation transport and illuminance distribution in spaces with venetian blinds. Sol. Energy 86(11), 3109–3124 (2012)

    Article  Google Scholar 

  17. Stanford University: Types of Ray Tracing. https://cs.stanford.edu/people/eroberts/courses/soco/projects/1997-98/ray-tracing/types.html. Accessed Oct 2018.

  18. Tabet, I.; Touafek, K.; Bellel, N.; Bouarroudj, N.; Khelifa, A.; Adouane, M.: Optimization of angle of inclination of the hybrid photovoltaic-thermal solar collector using particle swarm optimization algorithm. J. Renew. Sustain. Energy 6(5), 053116 (2014)

    Article  Google Scholar 

  19. Kennedy, J.; Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, Piscataway (1995)

  20. Leow, S.; Corrado, C.; Osborn, M.; Carter, S.: Analyzing luminescent solar concentrators with front-facing photovoltaic cells using. J. Appl. Phys. 113, 214510 (2013)

    Article  Google Scholar 

  21. Weisstein, E.W.: Reflection from Wolfram MathWorld. http://mathworld.wolfram.com/Reflection.html. Accessed 15 Oct 2018

  22. Helton, J.C.; Davis, F.J.: Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab. Eng. Syst. Saf. 81(1), 23–69 (2003)

    Article  Google Scholar 

  23. Helton, J.C.; Johnson, J.D.; Sallaberry, C.J.; Storlie, C.B.: Survey of sampling-based methods for uncertainty and sensitivity analysis. Reliab. Eng. Syst. Saf. 91(10), 1175–1209 (2006)

    Article  Google Scholar 

  24. McKay, M.D.; Beckman, R.J.; Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21, 239–245 (1979)

    MathSciNet  MATH  Google Scholar 

  25. Owen, A.: Quasi-Monte Carlo sampling. In: Monte Carlo Ray Tracing: SIGGRAPH 2003 Course 44, New York, ACM, pp. 69–88 (2003)

  26. Rehman, N.; Siddiqui, M.: Critical concentration ratio for solar thermoelectric generators. J. Electron. Mater. 45(10), 5285–5296 (2016)

    Article  Google Scholar 

  27. Rehman, N.; Siddiqui, M.: Performance model and sensitivity analysis for a solar thermoelectric generator. J. Electron. Mater. 46(3), 1794–1805 (2017)

    Article  Google Scholar 

  28. Rehman, N.; Uzair, M.; Siddiqui, M.; Khamooshi, M.: Regression models and sensitivity analysis for the thermal performance of solar flat-plate collectors. Arab. J. Sci. Eng. 44(2), 1119–1127 (2019)

    Article  Google Scholar 

  29. Uzair, M.; Rehman, N.; Raza, S.: Probabilistic approach for estimating heat fluid exit temperature correlation in a linear parabolic trough solar collector. J. Mech. Sci. Technol. 32(1), 447–453 (2018)

    Article  Google Scholar 

  30. Mezura-Montes, E.; Coello, C.: Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evolut. Comput. 1(4), 173–194 (2011)

    Article  Google Scholar 

  31. Mohandes, M.: Modeling global solar radiation using particle swarm optimization (PSO). Sol. Energy 86(11), 3137–3145 (2012)

    Article  Google Scholar 

  32. Google: Google SketchUp—3D Modeling for Everyone. https://www.sketchup.com/. Accessed 28 May 2018

  33. Rehman, N.; Uzair, M.: Optimizing the inclined field for solar photovoltaic arrays. Renew. Energy 153, 280–289 (2020)

    Article  Google Scholar 

  34. Rehman, N.U.M.; Allauddin, U.: An optical-energy model for optimizing the geometrical layout of solar photovoltaic arrays in a constrained field. Renew. Energy 149, 55–65 (2020)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering Trades and Technology, Southern Institute of Technology, Invercargill, 9840, New Zealand

    N. U. Rehman

  2. Department of Mechanical Engineering, Auckland University of Technology, Auckland, New Zealand

    N. U. Rehman

  3. Department of Mechanical Engineering, NED University of Engineering and Technology, Karachi, Pakistan

    M. Uzair

Authors
  1. N. U. Rehman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Uzair
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. U. Rehman.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rehman, N.U., Uzair, M. Hybrid Ray Tracing Model and Particle Swarm Optimization for the Performance of an Internally Reflecting Solar Still with a Booster Reflector. Arab J Sci Eng 46, 2021–2032 (2021). https://doi.org/10.1007/s13369-020-04963-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-020-04963-z

Keywords

Search

Navigation