Comparative Study of Gravitational Water Vortex Turbine(GWVT) with Fibonaccian and Conical Casing

Abstract

A gravitational vortex turbine is an eco-friendly micro hydropower generation turbine that operates in ultra-low heads to provide energy in rural areas. Nowadays, the challenging aspects of conical casing vortex turbines are low efficiency and poor vortex dynamics. This paper focuses on a conceptual idea study that serves as a comparison of the results of a self-developed golden ratio spiral-based casing for an ultra-low head vortex turbine to a conical gravitational turbine using SolidWorks flow simulation. A six-blade rear turbine is used for the overall simulation. The turbine is placed at the outlet of the casing, and the values of force acting on the turbine blades are simulated. The torque at the turbine blade is also determined for the generic conical casing and the Fibonaccian casing, which are compared for the results. The relative pressure contour acting on the blades of the turbine is represented in a pictorial form. The torque is compared at each axis and plotted in a graphical format. The results encourage further development of GWVT, as there is an increase in the overall torque and efficiency.

Introduction

Electricity generation from green and renewable sources is crucial for the future, and Gravitational Water Vortex Turbines (GWVT) offer a cost-effective, ultra-low-head (0.7–3 m) solution, ideal for small rivers in hilly and plain regions. GWVTs harness free vortex flow—naturally formed by water entering a cylindrical or conical casing—to convert water’s kinetic energy into rotational energy via a turbine and alternator.

Two main methods exist for electricity generation using GWVT: bypass (diverting water) and open canal installation. Research shows GWVTs outperform small undershot water wheels in power output and efficiency, often reaching 30–50%. Key design factors affecting performance include blade number (5 blades optimal), blade angle, basin shape (conical preferred over cylindrical), and multi-stage configurations.

This study uniquely explores incorporating a Fibonacci spiral design in the turbine casing, inspired by natural vortex patterns like hurricanes, to improve flow dynamics. Using SolidWorks CFD simulations, a Fibonacci spiral casing (with specific parametric equations based on the golden ratio) is compared against a conventional conical casing, both with a 6-blade impeller angled at 40°. Simulation results show the Fibonacci casing generates higher relative pressure on turbine blades (max ~9500 Pa) compared to the conical casing (~6800 Pa), indicating potentially better efficiency and torque.

Overall, this approach aims to optimize GWVT performance, leveraging nature-inspired designs to enhance renewable energy generation from small water sources.

Conclusion

The discussion above reveals various concepts about the comparison between Fibonaccian casing and conical casing while used in gravitational watervortex turbines. Theaverage relative pressure of the Fibonaccian casing is higher due to the guided structure present in the Fibonacciancasingsattaining a maximum average relative pressure of 8950 Paat a volume rate of 0.06 m3/s while the maximum average relative pressureat a volume flow of 0.06 m3/s is 7050 Pa in the conical casing;thus, it shows 21% higher relative pressure is achieved in the Fibonaccian casing. The torque inthe Y axis does not contribute to the rotation of the turbine. The torque in the X axis is higher in the Fibonaccian casing than in the conical casing, as the maximum value of X torque in the Fibonaccian casing is2.1484 Nm and in the conical casing is 1.4897Nm which is 30% higher. The difference in the torque generated in the Z direction between the 2 casings is relatively very small the Fibonaccian casing which has a small increase in net torque when compared to the conical casing as the maximum value ofZ torque in the Fibonaccian casing is 0.1267Nm and in the conical casing is 0.0686 Nm, which is 45% higher. The relative pressure and the torque acting on the turbine directly affect the angular velocity of the impeller and the torque generated by the turbine which is directly proportional to the efficiency of the turbine.With higher pressure, optimized flow guidance, and greater torque, the Fibonaccian casing achieves an efficiency of 8.47%, whereas the conical casing reaches 7.37 %. This increase in efficiency demonstrates the enhanced energy conversion efficiency of the Fibonaccian casing than the conical casing. The manufacturing process of Fibonaccian casing is a bittricky, the complex structure makes it only manufacturable using 3D printing or printing a Mold using 3D printing and casting the cement into it.

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Copyright

Copyright © 2025 Arunesh Muthiah K, Jai Harish D, Ajmal Batcha S, Sreeharan B N. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.