An analytical model for rotors in confined flow across operating regimes

Abstract: Rotors operating in confined flows, or blockage, are commonly encountered in wind and water tunnels, as well as in shallow or dense deployments of hydrokinetic turbines. Confinement induces a streamwise pressure gradient in the channel, modifying the rotor induction, thrust, and power. To account for these effects, physics-based or empirical blockage corrections are used as a transfer function between the dynamics of an object operating in confined and unconfined settings. However, existing blockage models are largely only applicable to rotors operating at relatively low thrust coefficients, such that the assumptions of classical momentum theory are valid. Further, rotors are often partially misaligned with the inflow, which modifies both the geometric blockage and the thrust force, whereas existing blockage models assume perfectly aligned flow conditions. We develop a generalised engineering model for an actuator disk operating in confined flow at arbitrary misalignment angles and thrust coefficients, termed the Unified Blockage Model. The analytical model shows excellent agreement with large eddy simulations of an actuator disk and elucidates the coupled interactions between thrust, misalignment, and blockage. To predict bladed rotor dynamics, the Unified Blockage Model is incorporated into a blade element momentum (BEM) model framework and validated against blade-resolved simulations across a wide range of tip-speed and blockage ratios. Finally, a blockage correction method is developed based on the Unified Blockage Model and validated against a suite of numerical and experimental data.