Investigation and optimization of the performance of gravity water wheels

Water wheels are rotating hydraulic machines that were introduced thousands of years ago to generate energy from water. Gravity water wheels are driven by the weight of the water flow and a portion of the flow kinetic energy. In the last decades, due to the increasing diffusion of micro hydropower plants (installed power less than 100 kW), gravity water wheels are being recognized as attractive hydraulic machines to produce electricity. Unfortunately, most of the engineering knowledge on water wheels is dated back to the XIX century, with several gaps and uncertainty. Additional work is still needed to fully understand the power losses and the performance within water wheels, that could lead to further improvements in efficiency. The scope of the present thesis is the investigation and improvement of the performance of gravity water wheels. This aim was achieved using physical experiments to quantify water wheels performance under different hydraulic conditions, theoretical models to estimate and predict the efficiency, and numerical simulations to optimize the design. Undershot, breastshot and overshot water wheels were investigated, in order to give a wide overview on all the kinds of gravity water wheels. Sagebien and Zuppinger undershot wheels were investigated at Southampton University, under the supervision of prof. Gerald Muller, from October 2015 until April 2016. These two wheels differ based on the shape of the blades. The blades of Sagebien wheels are optimized to reduce the inflow power losses, while those of Zuppinger wheels are conceived to minimize the outflow power losses. The objective of the experiments was to understand which of the two designs is better in term of efficiency. The tests showed that the Sagebien type exhibits a more constant efficiency as a function of the flow rate and the hydraulic head than the Zuppinger type. The maximum efficiency (excluding leakages) was identified as 88%. Breastshot water wheels were investigated experimentally, theoretically and using numerical Computational Fluid Dynamic (CFD) methods at Politecnico di Torino. The maximum experimental efficiency was estimated as 75% using a sluice gate inflow. A vertical inflow weir was also investigated, and found to have a more constant efficiency versus the rotational speed of the wheel, but with similar maximum values. A theoretical model that was developed to estimate the power output, power losses and efficiency, had a discrepancy with the experiments of 8%. A dimensionless law was also developed to estimate the power output. Numerical CFD simulations were performed to understand the effects of the number and shape of the blades on the efficiency. The optimal number of blades was 48 for the investigated wheel, and the efficiency can be improved using a circular shape. The numerical discrepancy with experiments was less than 6%. Overshot water wheels were investigated using a similar approach as done for breastshot wheels, and were found to have a maximum experimental efficiency of 85%. A theoretical model was developed to estimate the power losses and the efficiency, in particular to quantify the volumetric losses at the top of the wheel, that is the fraction of the flow which can not enter into the buckets and that is lost. Then, numerical simulations will be started to try to improve the wheel efficiency, reducing the previous volumetric losses. More specifically, a circular wall around the periphery of the wheel was added to the original design, leading to a performance improvement up to 60%. The results of this work show that water wheels can be considered attractive hydropower converters