Model selection and performance evaluation of solar chimney systems using CFD and multivariate analysis with Chernoff faces
This paper presents an integrated study combining computational fluid dynamics (CFD) and multivariate statistical analysis for solar chimney optimization. The Manzanares plant was adopted as a reference model and simulated in ANSYS Fluent to generate a dataset for parametric evaluation. Eleven regression models were examined to describe air velocity as a function of the scale parameter, and their formulations were validated using statistical metrics and graphical multivariate analysis. The methodology introduces Chernoff faces as a visual–statistical tool to encode multiple performance indicators per model, enabling a structured comparison beyond conventional criteria. The powerlaw model proved the most suitable, showing strong goodness-of-fit, physical consistency, and stable behavior across scenarios. Specific equations were derived for different irradiance levels, and system efficiency and power output were estimated and compared with previous studies. The results confirm that geometric down-scaling significantly reduces performance. The proposed visual–statistical framework provides a robust and interpretable approach for model selection and performance assessment in solar energy systems, offering a novel and reproducible multivariate strategy for engineering design and optimization.
1. Pinto Santos AR, Cortés Peña OF. ¿Qué piensan los estudiantes universitarios frente a la formación investigativa? REDU. Revista de Docencia Universitaria. 2017;15(2):57-75. https://doi.org/10.4995/redu.2017.6059
2. Chernoff H. The Use of Faces to Represent Points in k-Dimensional Space Graphically. J Am Stat Assoc. 1973;68(342):361-368. https://doi.org/10.1080/01621459.1973.10482434
3. Flury B, Riedwyl H. Graphical Representation of Multivariate Data by Means of Asymmetrical Faces. J Am Stat Assoc. 1981;76(376):757-765. https://doi.org/10.1080/01621459.1981.10477718
4. Hananel A, Loaiza S, Collantes L. Enhancing academic performance of engineering students: A multivariate statistical analysis of grades in a Mathematics course. Interact. Des. Archit.(s). 2024;63:268-299. https://doi.org/10.55612/s-5002-063-012
5. Olmos EG. Students performance: A methodology for its measurement. Economía. 1997;22(13):7-25. Accessed Jun 18, 2026. https://EconPapers.repec.org/RePEc:ula:econom:v:22:y:1997:i:13:p:7-25.
6. Haaf W, Friedrich K, Mayr G, Schlaich J. Solar chimneys part I: principle and construction of the pilot plant in Manzanares. Int J Sol Energy. 1983;2(1):3-20. http://doi.org/10.1080/01425918308909911
7. Herrada H, Jiménez M. In situ measurement of heat transfer coefficient and solar aperture of insulated dwellings using the dynamic integrated method. Appl Therm Eng. 2022;200. https://doi.org/10.1016/j.applthermaleng.2021.117644
8. Avial M, Chourio E, Casadei Carniel L, Vargas Z. El software matemático como herramienta para el desarrollo de habilidades del pensamiento y el mejoramiento del aprendizaje de las matemáticas. Rev Electrón Actual Investig Educ. 2007;7. Accessed Jun 18, 2026. https://www.redalyc.org/pdf/447/44770209.pdf.
9. Medina Martínez NF. Las variables complejas en investigaciones pedagógicas. Apuntes Universitarios. 2015;5(2):9-18. https://doi.org/10.17162/au.v0i2.244
10. Xu Y, Zhou X. Performance of divergent-chimney solar power plants. Sol Energy. 2018;170:379-387. https://doi.org/10.1016/j.solener.2018.05.068
11. Hu S, Leung DYC, Chan JCY. Numerical modelling and comparison of the performance of diffuser-type solar chimneys for power generation. Appl Energy. 2017;204:948-957. https://doi.org/10.1016/j.apenergy.2017.03.040
12. Mebarki A, Sekhri A, Assassi A, Hanafi A, Marir B. CFD analysis of solar chimney power plant: Finding a relationship between model minimization and its performance for use in urban areas. Energy Rep. 2022;8:500-513. https://doi.org/10.1016/j.egyr.2021.12.008
13. Murena F, Gaggiano I, Mele B. Fluid dynamic performances of a solar chimney plant: Analysis of experimental data and CFD modelling. Energy. 2022;249. https://doi.org/10.1016/j.energy.2022.123
14. Cuce E, Cuce PM, Carlucci S, et al. Solar Chimney Power Plants: A Review of the Concepts, Designs and Performances. Sustainability. 2022;14(3):1450. https://doi.org/10.3390/su14031450
15. Biswas N, Mandal DK, Bose S, Manna NK, Benim AC. Experimental Treatment of Solar Chimney Power Plant—A Comprehensive Review. Energies. 2023;16(17):6134. https://doi.org/10.3390/en16176134
16. Mehranfar S, Gharehghani A, Azizi A, Mahmoudzadeh Andwari A, Pesyridis A, Jouhara H. Comparative assessment of innovative methods to improve solar chimney power plant efficiency. Sustain Energy Technol Assess. 2022;49:101807. https://doi.org/10.1016/j.seta.2021.101807
17. Zhu L, Khdair AI, Aghaei A, Zalipour K, Chen H, Afrand M. A comprehensive review of solar chimney power plants: technology, performance, and future prospects. Sustain Energy Technol Assess. 2025;81:104413. https://doi.org/10.1016/j.seta.2025.104413
18. Xiong H, Ming T, Shi T, et al. Numerical investigation on performance of solar chimney power plant with three wind resistant structures. Energy. 2024;297:131262. https://doi.org/10.1016/j.energy.2024.131262
19. Rahimi-Larki M, Arefian A, Nazari S, Torkfar A, Hosseini-Abardeh R, Sarlak H. Performance investigation of a sloped collector solar chimney system exposed to the ambient crosswind. Energy. 2025;318:134732. https://doi.org/10.1016/j.energy.2025.134732
20. Maia CB, Castro Silva JdO. CFD Analysis of a Small-Scale Solar Chimney Exposed to Ambient Crosswind. Sustainability. 2022;14(22):15208. https://doi.org/10.3390/su142215208
21. Arefian A, Hosseini-Abardeh R, Rahimi-Larki M, Torkfar A, Sarlak H. A comprehensive analysis of time-dependent performance of a solar chimney power plant equipped with a thermal energy storage system. Renew Sustain Energy Rev. 2024;189:114051. https://doi.org/10.1016/j.rser.2023.114051
22. Huang S, Li W, Lu J, Li Y, Wang Z, Zhu S. Experimental study on thermal performances of a solar chimney with and without PCM under different system inclination angles. Energy. 2024;290:130154. https://doi.org/10.1016/j.energy.2023.130154
23. Esmail MFC, A-Elmagid WM, Mekhail T, Al-Helal IM, Shady M. A numerical comparative study of axial flow turbines for solar chimney power plant. Case Stud Therm Eng. 2021;26:101046. https://doi.org/10.1016/j.csite.2021.101046
24. Caicedo P, Wood D, Johansen C. Radial Turbine Design for Solar Chimney Power Plants. Energies. 2021;14(3):674. https://doi.org/10.3390/en14030674
25. Fertahi SE, Moeneclaey-Masson C, Guimerà R, Belarbi R, Revol E. CFD Validation in Solar Chimney Power Plants: A Comparison of Modeling Approaches. Fluids. 2024;9(11):251. https://doi.org/10.3390/fluids9110251
26. Cuce PM, Cuce E, Mandal DK, et al. ANN and CFD driven research on main performance characteristics of solar chimney power plants: Impact of chimney and collector angle. Case Stud Therm Eng. 2024;60:104568. https://doi.org/10.1016/j.csite.2024.104568
27. Mandal DK, Gupta KK, Biswas N, Manna NK, Santra S, Benim AC. Optimization of hybrid solar chimney power plants (HSCPPs): A review of multi-objective approaches. Appl Energy. 2025;396:126214. https://doi.org/10.1016/j.apenergy.2025.126214
28. Nie J, Guo TZ, Xu JC, Ruan XY, Nie LYM, Guo X. CFD-based multi-location analysis of power output and LCOE for solar chimneys in arid regions of Inner Mongolia. Case Stud Therm Eng. 2026;79:107726. https://doi.org/10.1016/j.csite.2026.107726
29. Salameh T, Zayed M, Juaidi A, Abdallah R, Hamid AK, Hussein M. CFD and technoeconomic analysis of site-dependent renewable trigeneration in solar chimney power plant. Int J Hydrogen Energy. 2026;205:153285. https://doi.org/10.1016/j.ijhydene.2025.153285
30. Velazco Lorenzo D, Butler Blacker JG. Desarrollo de un modelo experimental de una chimenea solar-eólica para suministro eléctrico. TECNIA. 2022;32(1):13-27. https://doi.org/10.21754/tecnia.v32i1.1092
31. Hananel A, Garcia R, Vera A. Optimization of solar chimney performance through CFD modelling and parametric experimental design. Int J Optim Control Theor Appl. 2026;16(2):428-449. https://doi.org/10.36922/IJOCTA025430181
32. Analysis of the driving potential of a solar chimney power plant. R&D J. 1999;15:85-94. Accessed Jun 18, 2026. http://www.scielo.org.za/scielo.php?script=sci_arttext&pid=S2309-89881999000100005&lng=en&nrm=iso.
33. Ming T, Liu W, Xu G. Analytical and numerical investigation of the solar chimney power plant systems. Int J Energy Res. 2006;30(11):861-873. https://doi.org/10.1002/er.1191
34. POWER NASA Project. The Prediction of Worldwide Energy Resource (POWER). NASA Applied Sciences Program within the Earth Science Division of the Science Mission Directorate; 2024. Accessed Jun 18, 2026. https://power.larc.nasa.gov/.
35. Danook SH, Al-bonsrulah HAZ, Hashim I, Veeman D. CFD Simulation of a 3D Solar Chimney Integrated with an Axial Turbine for Power Generation. Energies. 2021;14(18):5771. https://doi.org/10.3390/en14185771
36. Sundararaj M, Rajamurugu N, Anbarasi J, Yaknesh S, Sathyamurthy R. Parametric optimization of novel solar chimney power plant using response surface methodology. Results Eng. 2022;16:100633. https://doi.org/10.1016/j.rineng.2022.100633
37. Chrobak R, Sempere PG, Prieto AB, Avalos KR. Exploración sobre las estrategias de enseñanza de docentes de ingeniería para el logro de habilidades creativas e innovadoras en sus estudiantes.In: II Congreso Internacional de Investigación y Docencia de la Creatividad; online; 2017. https://doi.org/10.13140/RG.2.1.3061.9288
38. Cuce E, Sen H, Cuce PM. Numerical performance modelling of solar chimney power plants: Influence of chimney height for a pilot plant in Manzanares, Spain. Sustain Energy Technol Assess. 2020;39:100704. https://doi.org/10.1016/j.seta.2020.100704
39. Abo-Zahhad EM, Hachicha AA, Mistarihi MZ, Salim MH, Esmail MFC. Optimization of ground material properties for enhanced solar chimney power plant efficiency: A CFD and RSM approach. Energy Rep. 2025;13:3929-3945. https://doi.org/10.1016/j.egyr.2025.03.035
40. Torkfar A, Arefian A, Hosseini-Abardeh R, Bahrami M. Implementation of active and passive control strategies for power generation in a solar chimney power plant: A technical evaluation of Manzanares prototype. Renew Energy. 2023;216:118912. https://doi.org/10.1016/j.renene.2023.118912