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Screw turbine

## Summary

Archimedes Screw Generator (ASG),[1] also known as Archimedes/Archimedean Screw Turbine (AST),[2] Archimedean turbine or screw turbine is a hydraulic machine that convert the potential energy of water on an upstream level into work. This hydropower converter is driven by the weight of water, similar to water wheels, and can be considered as a quasi-static pressure machine.[2]

Reverse action of the "Archimedean screw", the principle of the "screw turbine" gaining energy from water flowing down through the screw.
Screw turbines typically have three or four flights (second row)
Two parallel screw turbines capable of producing 75 kW each, in Monmouth, Wales
Video of a 40 kW screw turbine in Munich, Germany

Archimedes screws can be used to generate power if they are driven by flowing fluid instead of lifting fluid.[2] Water transiting the screw from high to low elevation generates a torque on the helical plane surfaces, causing the screw to rotate.[2] The Archimedes screw generator consists of a rotor in the shape of an Archimedean screw which rotates in a semicircular trough. Water flows into the screw and its weight presses down onto the blades of the turbine, which in turn forces the turbine to turn. Water flows freely off the end of the screw into the river. The upper end of the screw is connected to a generator through a gearbox. The Archimedes screw is theoretically a reversible hydraulic machine, and there are examples of single installations where screws can be used alternately as pumps and generators.[3]

The required parameters to design Archimedes screws.[3] The Archimedes screw design parameters are similar in designing Archimedes screw turbines (generators) and Archimedean screw pumps [1].

## History

A screw turbine at a small hydro power plant in Goryn, Poland.

The Archimedean screw is an ancient invention, attributed to Archimedes of Syracuse (287–212 BC.), and commonly used to raise water from a watercourse for irrigation purposes. In 1819 the French engineer Claude Louis Marie Henri Navier (1785–1836) suggested using the Archimedean screw as a type of water wheel. In 1916 William Moerscher applied for a U.S. patent on the hydrodynamic screw turbine.[4]

## Application

12 kW screw turbine at the Cragside estate

The Archimedean screw turbine is applied on rivers with a relatively low head (from 0.1 m to 10 m)[2] and on low flows (0.01 m³/s up to around 10 m³/s on one turbine). Due to the construction and slow movement of the blades of the turbine, the turbine is considered to be friendly to aquatic wildlife. It is often labelled as "fish friendly". The Archimedean turbine may be used in situations where there is a stipulation for the preservation and care of the environment and wildlife.

## Design

An Archimedes Screw Turbine (AST) hydroelectricity powerplant can be considered as a system with three major components: a reservoir, a weir, and the AST (which is connected to the system by a control gate and trash rack).[2] At most real AST locations, the incoming flow must be divided between the AST and a parallel weir. Typically, a minimum flow over the weir is mandated for the protection of the local environment. Other outlets as well as a fish ladder could be considered as the other components of this system.[2] A comprehensive guide about the principles of designing Archimedes screw turbines and screw hydropower plants is available in "Archimedes Screw Turbines: A Sustainable Development Solution for Green and Renewable Energy Generation—A Review of Potential and Design Procedures".[2]

### Flow Rate Model

To design Archimedes screw turbines and hydropower plants, it is essential to estimate the amount of water is passing through the screw turbine since the amount of power generated by an Archimedes screw turbine is proportional to the volume flow rate of water through it.[2] The volume of water that enters an Archimedes screw turbine depends on the inlet water depth and the screw's rotation speed.[5] To estimates the total flow rate passing through an Archimedes screw turbine for different rotation speeds (ω) and inlet water levels the following equation could be used:[2][5]

${\displaystyle Q=\alpha Q_{Max}(A_{E}/A_{Max})^{\beta }(\omega /\omega _{M})^{\gamma }}$

Where ${\displaystyle \alpha }$ , ${\displaystyle \beta }$  and ${\displaystyle \gamma }$  are constants related to the screw properties. Preliminary investigations suggest that ${\displaystyle \alpha =1.242}$  , ${\displaystyle \beta =1.311}$  , and ${\displaystyle \gamma =0.822}$  give reasonable predictions of ${\displaystyle Q}$  for a wide range of small to full-scale AST sizes.[2][5]

### Design Archimedes screw geometry

By determination of ${\displaystyle D_{O}}$  other design parameters of Archimedes screws could be easily calculated using an easy an step by step analytical method.[1][3] Studies shows that the volume of flow passes through Archimedes screws is a function of inlet depth, diameter and rotation speed of the screw.[5][2] Therefore, the desired volumetric flow rate ${\displaystyle Q}$  in ${\displaystyle (m^{3}/s)}$  and rotation speed ${\displaystyle \omega }$  in ${\displaystyle (rad/s)}$  the following analytical equation could be used to determinate the Archimedes screws overall diameter ${\displaystyle D_{O}}$  in ${\displaystyle (m)}$ :[1]

${\displaystyle D_{O}=(16\pi Q}/{\sigma \omega (2\theta _{O}-sin2\theta _{O})-\delta ^{2}(2\theta _{i}-sin(2\theta _{i}))^{1/3}}$

Based on the common standards that the Archimedes screw designers use this analytical equation could be simplified as:[1]

${\displaystyle D_{O}=\eta Q^{3/7}}$

The value of η could simply determinate using the ${\displaystyle \eta }$  graph[1] or ${\displaystyle \Theta }$  graph.[3] By determination of ${\displaystyle D_{O}}$  other design parameters of Archimedes screws could be easily calculated using an easy an step by step analytical method.[1][3]

## Examples

### In the United States

• The first Archimedes screw turbine was installed in Canada in 2013 near Waterford, Ontario.[2]

## Literature

• YoosefDoost, A, W.-D. Lubitz: Design Guideline for Hydropower Plants Using One or Multiple Archimedes Screws, Processes, 2021. doi:10.3390/pr9122128
• YoosefDoost, A, W.-D. Lubitz: Archimedes Screw Design: An Analytical Model for Rapid Estimation of Archimedes Screw Geometry, Energies 2021. doi:10.3390/en14227812
• YoosefDoost, A, W.-D. Lubitz: Archimedes Screw Turbines: A Sustainable Development Solution for Green and Renewable Energy Generation—A Review of Potential and Design Procedures, Sustainability, 2020. doi:10.3390/su12187352.
• P. J. Kantert: Manual for Archimedean Screw Pump, Hirthammer Verlag 2008, ISBN 978-3-88721-896-6
• P. J. Kantert: Praxishandbuch Schneckenpumpe. Hirthammer Verlag 2008, ISBN 978-3-88721-202-5
• William Moerscher - Patent US1434138
• K. Brada, K.-A. Radlik - Water Screw Motor to Micro Power Plant - First Experiences of Construction and Operation (1998)
• K. Brada - Micro Power Plant with Water Screw Motor (1995)
• K. Brada, K.-A. Radlik - Water Power Screw - Characteristic and Use (1996)
• K. Brada, K.-A. Radlik, (1996). Water screw motor for micropower plant. 6th Intl. Symp. Heat exchange and renewable energy sources, 43–52, W. Nowak, ed. Wydaw Politechniki Szczecińskiej, Szczecin, Poland.

## References

1. YoosefDoost, Arash; Lubitz, William David (January 2021). "Archimedes Screw Design: An Analytical Model for Rapid Estimation of Archimedes Screw Geometry". Energies. 14 (22): 7812. doi:10.3390/en14227812.
2. YoosefDoost, Arash; Lubitz, William David (2020). "Archimedes Screw Turbines: A Sustainable Development Solution for Green and Renewable Energy Generation—A Review of Potential and Design Procedures". Sustainability. 12 (18): 7352. doi:10.3390/su12187352.   Text was copied from this source, which is available under a Creative Commons Attribution 4.0 International License.
3. YoosefDoost, Arash; Lubitz, William David (December 2021). "Design Guideline for Hydropower Plants Using One or Multiple Archimedes Screws". Processes. 9 (12): 2128. doi:10.3390/pr9122128.
4. ^ William Moerscher, Water-power system, U.S. Patent 1,434,138, granted Oct 31, 1922.
5. ^ a b c d YoosefDoost, Arash; Lubitz, William David (2021), Ting, David S.-K.; Vasel-Be-Hagh, Ahmad (eds.), "Development of an Equation for the Volume of Flow Passing Through an Archimedes Screw Turbine", Sustaining Tomorrow, Cham: Springer International Publishing, pp. 17–37, doi:10.1007/978-3-030-64715-5_2, ISBN 978-3-030-64714-8, S2CID 234121383, retrieved 2021-02-09
6. ^ "Woolston | Planning Application". Warrington Borough Council. Retrieved 2021-03-22.
7. ^ "Woolston | Project Overview". renfin.eu. Retrieved 2021-03-22.
8. ^ "Woolston | Local News Items". Warrington Worldwide. Retrieved 2021-03-22.
9. ^ "Totnes | MannPower Consulting". www.mannpower-hydro.co.uk. Retrieved 2016-08-05.
10. ^ "Romney | MannPower Consulting". www.mannpower-hydro.co.uk. Retrieved 2016-08-05.
11. ^ "Bealeys Weir | MannPower Consulting". www.mannpower-hydro.co.uk. Retrieved 2016-08-05.
12. "Hydro Power Case Studies, Micro-Hydro Case Studies - Western Renewable Energy". www.westernrenew.co.uk. Retrieved 2016-08-05.
13. ^ "Hydropower returns to Cragside". National Trust. Retrieved 2016-08-09.
14. ^ Andrew Ragall, Ancient technology in Meriden's Hannover Pond dam begins generating electricity, Meriden Record Journal, April 27, 2017.
15. ^ New England Hydropower Energizes First Archimedes Screw Turbine in U.S., PR Newswire, April 27, 2017.