Experimental identification of blade-level forces, torque, and pitching moment for cross-flow turbines

TL;DR

This paper develops a physics-based method to extract blade-level forces, torque, and pitching moment for cross-flow turbines from axis-of-rotation measurements. By decomposing turbine-level data into blade and support-structure contributions and validating against blade-only LES, it demonstrates strong agreement and reveals the critical role of the pitching moment, which can offset tangential power and drive downstream performance loss. The approach shows blade-level thrust and forces collapse across shaft configurations, highlights that the normal force dominates blade loading, and provides insights for blade design and cross-flow turbine modeling. The findings underscore the need to include pitching moment in analytical models and offer a framework for assessing structural loads and performance limits in cross-flow devices.

Abstract

Cross-flow turbine power is a net sum of power generation from rotating blades and power loss from rotating support structures. While the aggregate forces and torques at the turbine level are important for end use, these can inhibit a deeper understanding of fluid-structure interactions. Identification of blade-level forces and torques allows for specific investigations into how the fluid forcing on the blade drives rotation and can aid blade structural design. Here, we present a physics-based methodology for extracting blade-level forces and torques from experimental measurements at the axis of rotation of a cross-flow turbine, and demonstrate strong agreement with equivalent blade-only simulations. In doing so, we highlight the often-overlooked pitching moment, which offsets continuous increases in power generation from the tangential force and leads to net-zero power generation at freewheel.

Figures (16)

• Figure 1: (a) Cross-flow turbine overview with upstream and downstream sweeps indicated. (b) Blade-level kinematic definitions and blade-level coordinate system $(\hat{r},\hat{\theta})$. (c) Corresponding free body diagram and global coordinate system $(\hat{x},\hat{y})$.
• Figure 2: Conceptual representation of how the flow incident on the support structures may differ when (a) blades are present vs. (b) when absent.
• Figure 3: (a) Schematic of isolation of the blade-level forcing using the physics-based strategy. (b) Schematic of isolation of forcing on the struts.
• Figure 4: Schematics of the four different turbine shaft configurations tested: (a) "Baseline", (b) "Outer", (c) "Inner", and (d) "Full".
• Figure 5: (a) Phase-averaged, turbine-level tangential force and torque coefficients for $\lambda\:=\:2.4$ (b) Phase-averaged secondary tangential force oscillations after high-pass filtering. (c) Phase-averaged vortex shedding off of the central turbine shaft at $\lambda\:=\:2.4, \theta\:=\:201^\circ$. Vorticity field is computed from PIV data from SnortlandDownstream. Comparison between filtered and unfiltered, time-averaged (d) performance (e) thrust force, and (f) lateral force coefficients