Effects of free surface and water gravity on the stress-strain of tubular turbine blades

Abstract: Tubular turbines have been widely used to develop low-head hydraulic resources and tidal energy, due to their compact structure, straight flow channels, large flow capacity, and high hydraulic efficiency. However, the hydraulic vibration, fatigue damage and cracks of overflow components inevitably occur in actual operation, particularly for the low number of runner blades, the large blade area, and simple structural support. Previous studies are focused mainly on the hydraulic design and performance evaluation of tubular turbines for the prototypes using experiments or numerical simulation. Less reports remain on the free-surface fluctuations in the reservoir and the influence of water gravity on the performance of the turbine. It is a high demand to accurately reveal the internal flow state of tubular turbines for the direct causes of blade vibration and fatigue damage. Taking the tubular turbine (including the upstream and downstream reservoir areas) as the research object, a numerical simulation was performed on the internal-flow performance in a prototype machine considering the free surface and water gravity. The one-way fluid-structure coupling calculation was implemented for the stress-strain analysis of the runner blade under different operating conditions, in order to reveal the distribution along the circumferential direction during the rotation of the runner. The results were as follows. 1) The pressure in the tubular turbine increased significantly under the free surface and the water gravity, with the increase of the submerged depth. The blades experienced periodic pressure fluctuations in the process of rotation. The magnitude of pressure fluctuations on the blade surface also increased accordingly, when the submerged depth of the runner increased, as the water head decreased. Therefore, there was severe vibration on the blade surface, when the tubular turbine operated under the condition of ultra-low head. 2) There was a gradually increased deformation at different positions of the blade from the hub to the chamber of the runner along the radial direction. The maximum deformation position was located at the geometric lowest point of the blade near the shroud. There was consistent running in the direction of hydrostatic pressure and the dynamic water pressure on the blade along the entire circumferential direction, leading to the increased deformation of the blade, where the blade overcame the hydrostatic pressure with the rotation of the runner. Once the hydrostatic pressure was promoted the rotation of the blade, the dynamic water pressure on the blade surface and the hydrostatic pressure were in opposite directions, indicating a counteracting effect on the dynamic water pressure for the reduced deformation of the blade. Therefore, the maximum deformation of the blade occurred at the blade rim, when the blade was running in a horizontal position during bottom-to-top rotating from the bottom to the top of the runner chamber. 3) Since the blade of the tubular turbine was supposed as a cantilever beam structure with the fixed constraints at the hub, the stress on the blade near the shroud was relieved by a larger amount of deformation. There was no deformation of the blade near the hub, due to the fixed constraint of the pivot. As such, the maximum stress occurred at the root of the blade pivot. Therefore, the distribution of the equivalent stress on the blade increased, as the radius decreased. The water head can greatly contribute to the decrease in the submerged depth of the runner, which was reduced the hydrostatic pressure on the blade surface, where the load on the blade surface tended to decrease for the reduced maximum deformation and maximum equivalent stress on the blade at different positions of circumferential direction. The blades were prone to deformation and fatigue damage at the low operating head of the tubular turbine. The finding can provide theoretical support to the severe vibration of tubular turbines in the ultra-low head operation, particularly for the hydraulic design, operation, and maintenance of tubular turbines.