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Non-uniform resistance in optimising energy extraction from a flow
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DOI：10.1017/jfm.2026.11764.png)
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Abstract
En 中文
Extracting energy from a flow is a fundamental problem in fluid mechanics of significant practical engineering importance. To generate power from a flow; a resistance must be applied. Open questions remain on how to optimise this resistance; particularly for non-uniform flows. In this paper; we extend the multi-streamtube theory to address this gap. The extended theory allows for an arbitrary resistance distribution across an actuator strip (representing either a single turbine or an array of turbines) and is formulated as a power-coefficient maximisation problem to determine the optimal resistance distribution for both uniform and non-uniform flows. When the undisturbed kinetic energy flux projected onto the strip’s frontal area is used to normalise the extracted power; a uniform resistance maximises the resulting power coefficient for both uniform and non-uniform incoming flows. When the upstream kinetic energy flux of the flow through the strip is used for normalisation; the same optimisation result is obtained for uniform incoming flow; regardless of the assumed resistance distribution. However; for a non-uniform incoming flow; the optimal resistance distribution is non-uniform; with greater resistance applied in regions of higher velocity within the shear flow. This different optimisation result for non-uniform flow arises physically because the kinetic energy flux used in the second power-coefficient definition depends on the resistance applied across the strip; whereas the first does not. Two-dimensional direct numerical simulations are employed to examine the applicability and limitations of the multi-streamtube theory. The numerical and optimisation results together demonstrate that optimising the resistance distribution requires accounting not only for the non-uniformity of the incoming flow but also for the local flow variability around the strip.
Keywords:
channel flow
low-dimensional models
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