Skip to main content

Hydrodynamic screw parameter optimization for maximum power output


Considering the limited amount of fossil fuels, the use of small-scale renewable energy generators has been promoted in various regions. One of the tools for small-scale power generation is the hydrodynamic screw, known as a floating turbine, which can convert the potential and kinetic energy of water into mechanical energy. In this paper, an investigation on the conditions of hydrodynamic screw as Archimedes screw turbine for electricity generation in laboratory scale is presented. For this purpose, two different screws were fabricated and used to achieve the optimum conditions for power generation as laboratory samples. A central composite design, the most commonly used approach from resource surface methodology, was developed to improve the modeling and reduce the number of laboratory tests for the input data of the simulation model developed via Design Expert software. Design Expert software was used to calculate optimized points for each bolt considering the experimental results. The results indicated that a higher number of blades with a shorter pitch, together with an increased number of trapped buckets between two consecutive blades, could have a direct impact on the optimal performance of the turbines. The results of optimized points indicated that by setting the discharge value on 5.64 L/s and the screw installation slope on 28.49°, the power was calculated to be 66.71 W for screw no. 1. This parameter was found to be equal to 12.96 W for screw No. 2, when the flow rate value and the screw installation slope were set on 7 L/s and 32.74°, respectively. Finally, the results of the simulation were validated in the laboratory and found to be acceptable considering ‏ ± ‏ 5% error value. Our findings indicate that both physical factors—such as pitch of blades and number of blades—and environmental factors—such as the slope of installation and discharge volume—can significantly affect the energy generation.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Data availability

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.


  1. Bhattacharya, S. (2021). Central composite design for response surface methodology and its application in pharmacy. Response surface methodology in engineering science-IntechOpen.

  2. Bouvant, M., Betancour, J., Velásquez, L., Rubio-Clemente, A., & Chica, E. (2021). Design optimization of an Archimedes screw turbine for hydrokinetic applications using the response surface methodology. Renewable Energy, 172, 941–954.

    Article  Google Scholar 

  3. Box, G. E. P., & Wilson, K. B. (1951). On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society, Series B, 13, 1–38. Discussion: 3845.

    Google Scholar 

  4. Dellinger, G., Simmons, S., Lubitz, W. D., Garambois, P., & Dellinger, N. (2019). Effect of slope and number of blades on Archimedes screw generator power output. Renewable Energy, 136, 896–908.

    Article  Google Scholar 

  5. Deng, Z., Carlson, T. J., Double, D. D., & Ploskey, G. R. (2011). Fish passage assessment of an advanced hydropower turbine and conventional turbine using blade-strike modeling. Energies, 4, 57–67.

    Article  Google Scholar 

  6. Erinofiardi, E. (2014). Preliminary design of Archimedean screw turbine prototype for remote area power supply. Journal of Ocean Mechanical and Aerospace Science and Engineering (JOMAse), 5, 30–33.

    Google Scholar 

  7. Erinofiardi, E., Nuramal, A., Bismantolo, P., Date, A., Akbarzadeh, A., Manil, A. K., & Suryono, A. F. (2017). Experimental study of screw turbine performance based on different angle of inclination. Energy Procedia, 110, 8–13.

    Article  Google Scholar 

  8. Havn, T. B., Sæther, S. A., Thorstad, E. B., Teichert, M. A. K., Heermann, L., Diserud, O. H., Borcherding, J., Tambets, M., & Økland, F. (2017). Downstream migration of Atlantic salmon smolts past a low head hydropower station equippped with Archimedes screw and Francis turbines. Ecological Engineering, 105, 262–275.

    Article  Google Scholar 

  9. Horch, J. C. (1916). Proefnemingen met een watervijzel [Experiments with a water ram pump]. De Ingenieur, 49, 945–954. In German.

    Google Scholar 

  10. International Energy Agency (IEA). (2010). Annex-2: small scale hydropower Sub-Task B2 innovative technologies for smallscale hydro: summray report. Implementing agreement for hydropower technologies and programmes.

  11. Kantert, P. J. (2008). Praxishandbuch Schneckenpumpe: Ratgeber und Entscheidungshilfe fϋr Planer. Bauherren und Betreiber [Manual for Archamedian screw pump: guide and decision making aid for planners, builders and operators]. Deutsche Vereinigung für Wasserwirtschaft, Abwasser und Abfall. In German.

    Google Scholar 

  12. Kleijnen, J. P. (2015). Response surface methodology. Handbook of simulation optimization (pp. 81–104). Springer.

    Chapter  Google Scholar 

  13. Knížat, B., Csuka, Z., & Hyriak, M. (2016). Impeller design of a single blade hydrodynamic pump. AIP Conference Proceedings, 1768(1), 020034.

    Article  Google Scholar 

  14. Koetsier, T., & Blauwendraat, H. (2004). The Archimedean screw-pump: a note on its invention and the development of the theory. In M. Ceccarelli (Ed.), International Symposium on History of Machines and Mechanisms, pp. 181–194. Springer International Publishing.

  15. Kraybill, Z. (2013). Structural analysis of an Archimedes screw and a kinetic hydro turbine. Lehigh University.

    Google Scholar 

  16. Lavrič, H., Rihar, A., & Fišer, R. (2018). Simulation of electrical energy production in Archimedes screw-based ultra-low head small hydropower plant considering environment protection conditions and technical limitations. Energy, 164, 87–98.

    Article  Google Scholar 

  17. Lee, K. T., Kim, E. S., Chu, W. S., & Ahn, S. H. (2015). Design and 3D printing of controllable-pitch Archimedean screw for pico-hydropower generation. Journal of Mechanical Science and Technology, 29(11), 4851–4857.

    Article  Google Scholar 

  18. Lisicki, M., Lubitz, W. D., & Taylor, G. W. (2016). Optimal design and operation of Archimedes screw turbines using Bayesian optimization. Applied Energy, 183, 1404–1417.

    Article  Google Scholar 

  19. Loots, I., Van-Dijk, M., Barta, B., Van-Vuuren, S. J., & Bhagwon, J. N. (2015). A review of low head hydropower technologies and applications in South African context. Renewable and Sustainable Energy Reviews, 50, 1254–1268.

    Article  Google Scholar 

  20. Lubitz, W. D. (2014). Gap flow in Archimedes screws. In Proceedings of the Canadian Society for Mechanical Engineering (CSME), International Congress, Toronto, Canada, June 1–4.

  21. Lubitz, W. D., Lyons, M., & Simmons, S. (2014). Performance model of Archimedes screw hydro turbines with variable fill level. Journal of Hydraulic Engineering, 140(10), 04014050.

  22. Müller, G., & Senior, J. (2009). Simplified theory of Archimedean screws. Journal of Hydraulic Research, 47(5), 666–669.

    Article  Google Scholar 

  23. Muysken, J. (1932). Berekening van het nuttig effect van de vijzel [Calculation of the effectiveness of the screw]. De Ingenieur, 21, 77–91. In Dutch.

    Google Scholar 

  24. Myers, R. H., Khuri, A. I., & Carter, W. H. (1989). Response surface methodology: 1966–l988. Technometrics, 31(2), 137–157.

    Article  Google Scholar 

  25. Myers, R. H., Montgomery, D. C., & Anderson-Cook, C. M. (2016). Response surface methodology: Process and product optimization using designed experiments. Wiley.

    Google Scholar 

  26. Nagel, G., & Radlik, K. A. (1988). Wasserf orderschnecken: Planung, Bau und Betrieb von Wasserhebeanlagen [Screw pumps: planning, construction and operation of water raising systems]. Udo Pfriemer Buchverlag. In German.

    Google Scholar 

  27. Nuernbergk, D. M. (2017). Archimedes screw in the twenty-first century. In: C. Rorres (Ed.), Archimedes in the 21st century, trends in the history of science (pp. 113–124). Springer International Publishing, Birkhäuser, Cham.

  28. Nuernbergk, D. M., & Rorres, C. (2013). Analytical model for water inflow of an Archimedes screw used in hydropower generation. Journal of Hydraulic Engineering, 139(2), 213–220.

    Article  Google Scholar 

  29. Rohmer, J., Knittel, K., Sturtzer, G., Flieller, D., & Renaud, J. (2016). Modeling and experimental results of an Archimedes screw turbine. Renewable Energy, 94, 136–146.

    Article  Google Scholar 

  30. Rorres, C. (2000). The turn of the screw: Optimal design of an Archimedes screw. Journal of Hydraulic Engineering, 126(1), 72–80.

    Article  Google Scholar 

  31. Stergiopoulou, A., & Stergiopoulos, V. (2013). Archimedes in cephalonia and in Euripus strait: modern horizontal archimedean screw turbines for recovering marine power. Journal of Engineering Science & Technology Review, 6(1), 44–51.

  32. Stergiopoulou, A., Stergiopoulos, V., & Kalkani, E. (2013). Contributions to the study of hydrodynamic behavior of innovative Archimedean screw turbines recovering the hydro potential of watercourses and of coastal currents. In: Proceedings of the 13th International Conference on Environmental Science and Technology, CEST2013_0196, Athens, Greece.

  33. Stergiopoulou, A., Stergiopoulos, V., Pelikan, B., Kalkani, E., Liakopoulos, A., & Farsirotou, E. (2014). Archimedes in Cephalonia and in euripus strait: Towards some modern old Archimedean screw ideas for recovering Mediterranean Sea power. Journal Odysseus Environmental and Cultural Sustainability of the Mediterranean Region, 6, 21–43.

    Google Scholar 

  34. Waters, S. R. (2015). Analyzing the performance of the Archimedes screw turbine within tidal range technologies. Lancaster University.

    Google Scholar 

  35. Waters, S. R., & Aggidis, G. A. (2015). Over 200 years in review, revival of the Archimedean screw from pump to turbine. Renewable and Sustainable Energy Reviews, 51, 497–505.

    Article  Google Scholar 

  36. Williamson, S. J., Stark, B. H., & Booker, J. D. (2014). Low head Pico hydro turbine selection using a multi-criteria analysis. Renewable Energy, 61, 43–50.

    Article  Google Scholar 

  37. Zafirah-Rosly, C., Jamaludin, U. K., Suraya-Azahari, N., Nik-Mu’tasim, M. A., Oumer, A. N., & Rao, N. T. (2016). Parametric study on efficiency of Archimedes screw turbine. ARPN Journal of Engineering and Applied Sciences, 11(18), 10904–10908.

    Google Scholar 

  38. Zhu, D., & Deng, Z. (2017). Ultra-low-head hydroelectric technology: A review. Renewable and Sustainable Energy Reviews, 78, 23–30.

    Article  Google Scholar 

Download references


The authors would like to express their thanks to Dr. A. M. Zahedi for his dedication during the course of this research.

Author information



Corresponding author

Correspondence to H. Eskandariun.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file1 (DOCX 4664 KB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Eskandariun, H., Noorollahi, Y., Ghobadian, B. et al. Hydrodynamic screw parameter optimization for maximum power output. Int J Energ Water Res 5, 413–423 (2021).

Download citation


  • Hydrodynamic screw
  • Hydropower turbine
  • Laboratory scale
  • Optimization
  • Renewable energy