The hydrodynamics of cross-flow turbines are complex, and rapid changes in angle of attack lead to phase and rotation-rate dependent dynamic stall and vortex shedding. It is well known that dynamic stall is both sensitive to changes in inflow and operational conditions, as well as being stochastic in nature. Previous work has shown that the duration/severity of flow reversal and detachment during dynamic stall have a critical impact on cross-flow turbine power output. This work aims to understand the effect of cycle-to-cycle variations of these dynamics on turbine performance.
Two-component, planar particle image velocimetry data, obtained inside the turbine swept area, is examined in concert with simultaneously captured turbine performance data. Flow fields for optimal (maximum power generation) and sub-optimal rotation rates are investigated via a hierarchical clustering pipeline featuring a principal component analysis (PCA) preprocessor. The PCA preprocessor allows for clustering based on all of the dynamics present in a rich PIV data set, weighted by their importance, in an interpretable, low dimensional subspace. The results of the flow field clustering are compared to those from hierarchical clustering on the simultaneous turbine power output. In doing so, we seek to understand the extent of cycle-to-cycle variability in turbine power and flow-field hydrodynamics, as well as the links between the two. This analysis is of particular interest because phase-averaging is a common approach for post-processing experimental flow fields containing missing data points and measurement noise. However, this relies on the untested assumption that cycle-to-cycle variations in the hydrodynamics are negligible with respect to performance. Unlike more simplistic statistical methods, the developed clustering techniques require few assumptions and are able to not only consider overall variation in the data but also differing trajectories in the power measurements and flow-field dynamics.
The data set utilized here has relatively small power variations overall (standard deviations on the order of 1.5% of the mean), yet our results show a clear power and hydrodynamic dependence on assigned cluster. Notably, both the flow-field and power clustering highlight a phase shift in the power production trajectories between the clusters, with the better performing cluster featuring a larger peak power value occurring earlier in the turbine rotation. Additionally, the better performing cluster exhibits earlier vortex shedding. In both cases, correlations between assigned cluster and inflow velocity are likely explanatory. While turbine power output is dependent on cluster, the differences in time averaged power between the clusters is small, on the order of 1.5%. This suggests that, for these conditions, phase averaging is an effective tool for investigating general trends and system understanding, but these clustering methods are useful aids for more nuanced analyses that link flow fields to power performance.