energies Article Archimedes Screw Design: An Analytical Model for Rapid Estimation of Archimedes Screw Geometry Arash YoosefDoost * and William David Lubitz   Citation: YoosefDoost, A.; Lubitz, W.D. Archimedes Screw Design: An Analytical Model for Rapid Estimation of Archimedes Screw Geometry. Energies 2021, 14, 7812. https://doi.org/10.3390/ en14227812 Academic Editors: Tomasz Wegiel and Dariusz Borkowski Received: 29 October 2021 Accepted: 12 November 2021 Published: 22 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). School of Engineering, University of Guelph, 50 Stone Rd E, Guelph, ON N1G 2W1, Canada; wlubitz@uoguelph.ca * Correspondence: YoosefDoost@Gmail.com or ArashYD@UoGuelph.ca Abstract: In designing Archimedes screws, determination of the geometry is among the fundamental questions that may affect many aspects of the Archimedes screw powerplant. Most plants are run- of-river and highly depend on local flow duration curves that vary from river to river. An ability to rapidly produce realistic estimations for the initial design of a site-specific Archimedes screw plant helps to facilitate and accelerate the optimization of the powerplant design. An analytical method in the form of a single equation was developed to rapidly and easily estimate the Archimedes screw geometry for a specific site. This analytical equation was developed based on the accepted, proved or reported common designs characteristics of Archimedes screws. It was then evaluated by comparison of equation predictions to existing Archimedes screw hydropower plant installations. The evaluation results indicate a high correlation and reasonable relative difference. Use of the equation eliminates or simplifies several design steps and loops and accelerates the development of initial design estimations of Archimedes screw generators dramatically. Moreover, it helps to dramatically reduce one of the most significant burdens of small projects: the nonscalable initial investigation costs and enables rapid estimation of the feasibility of Archimedes screw powerplants at many potential sites. Keywords: Archimedes screw design; analytical equation; quick estimation method; Archimedean screw; generator; turbine; fish safe/friendly; small/micro/pico hydropower plant; run of river powerplant; low head hydropower 1. Introduction The Archimedes screw (also known as an Archimedean or hydrodynamic screw) is one of the earliest hydraulic machines [1]. Using Archimedes screws as water pumps dates back many centuries. In the modern world, Archimedes screw pumps (ASP) are widely used in wastewater treatment plants and for dewatering low-lying regions. The Archimedes screw generator (ASG) is a safer hydropower technology for aquatic life, especially fish [2–9], that has been in use since the 1990s [10]. The Archimedes screw is a reversible hydraulic machine, and there are several examples of Archimedes screw installations where the screw can operate at different times as either pump or generator, depending on needs for power and watercourse flow [11]. When designing an ASG, estimation of the screw geometry is a fundamental necessity. The screw geometry affects many aspects of an Archimedes screw powerplant design. Each site has different specifications and limitations, including head, flow and available lo- cations for the power plant installation. Most ASG installations are run-of-river, with small or no reservoirs, and plant performance is directly dependent on the local flow duration curve which varies from river to river. The lack of active water storage in run-of-river (ROR) powerplants makes the importance of the temporal distribution of volumetric flow rate an important design parameter. This means that ASG designs must be highly site-specific, requiring different designs to account for site-specific characteristics. Energies 2021, 14, 7812. https://doi.org/10.3390/en14227812 https://www.mdpi.com/journal/energies